Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(8,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.12 | ||
Character | \(\chi\) | \(=\) | 35.22 |
Dual form | 35.5.g.a.8.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.12784 | + | 5.12784i | 1.28196 | + | 1.28196i | 0.939551 | + | 0.342408i | \(0.111242\pi\) |
0.342408 | + | 0.939551i | \(0.388758\pi\) | |||||||
\(3\) | 10.3372 | − | 10.3372i | 1.14858 | − | 1.14858i | 0.161749 | − | 0.986832i | \(-0.448287\pi\) |
0.986832 | − | 0.161749i | \(-0.0517134\pi\) | |||||||
\(4\) | 36.5894i | 2.28684i | ||||||||
\(5\) | −22.2980 | − | 11.3048i | −0.891922 | − | 0.452190i | ||||
\(6\) | 106.015 | 2.94487 | ||||||||
\(7\) | 13.0958 | + | 13.0958i | 0.267261 | + | 0.267261i | ||||
\(8\) | −105.579 | + | 105.579i | −1.64968 | + | 1.64968i | ||||
\(9\) | − | 132.716i | − | 1.63848i | ||||||
\(10\) | −56.3718 | − | 172.310i | −0.563718 | − | 1.72310i | ||||
\(11\) | −135.891 | −1.12306 | −0.561532 | − | 0.827455i | \(-0.689788\pi\) | ||||
−0.561532 | + | 0.827455i | \(0.689788\pi\) | |||||||
\(12\) | 378.233 | + | 378.233i | 2.62662 | + | 2.62662i | ||||
\(13\) | −35.4752 | + | 35.4752i | −0.209913 | + | 0.209913i | −0.804230 | − | 0.594318i | \(-0.797422\pi\) |
0.594318 | + | 0.804230i | \(0.297422\pi\) | |||||||
\(14\) | 134.306i | 0.685236i | ||||||||
\(15\) | −347.360 | + | 113.640i | −1.54382 | + | 0.505067i | ||||
\(16\) | −497.356 | −1.94280 | ||||||||
\(17\) | 146.269 | + | 146.269i | 0.506120 | + | 0.506120i | 0.913333 | − | 0.407213i | \(-0.133499\pi\) |
−0.407213 | + | 0.913333i | \(0.633499\pi\) | |||||||
\(18\) | 680.549 | − | 680.549i | 2.10046 | − | 2.10046i | ||||
\(19\) | − | 408.482i | − | 1.13153i | −0.824567 | − | 0.565764i | \(-0.808581\pi\) | ||
0.824567 | − | 0.565764i | \(-0.191419\pi\) | |||||||
\(20\) | 413.634 | − | 815.873i | 1.03409 | − | 2.03968i | ||||
\(21\) | 270.749 | 0.613942 | ||||||||
\(22\) | −696.826 | − | 696.826i | −1.43972 | − | 1.43972i | ||||
\(23\) | 212.278 | − | 212.278i | 0.401281 | − | 0.401281i | −0.477403 | − | 0.878684i | \(-0.658422\pi\) |
0.878684 | + | 0.477403i | \(0.158422\pi\) | |||||||
\(24\) | 2182.79i | 3.78957i | ||||||||
\(25\) | 369.405 | + | 504.148i | 0.591048 | + | 0.806636i | ||||
\(26\) | −363.822 | −0.538199 | ||||||||
\(27\) | −534.605 | − | 534.605i | −0.733340 | − | 0.733340i | ||||
\(28\) | −479.168 | + | 479.168i | −0.611184 | + | 0.611184i | ||||
\(29\) | 195.559i | 0.232531i | 0.993218 | + | 0.116266i | \(0.0370924\pi\) | ||||
−0.993218 | + | 0.116266i | \(0.962908\pi\) | |||||||
\(30\) | −2363.93 | − | 1198.48i | −2.62659 | − | 1.33164i | ||||
\(31\) | 965.178 | 1.00435 | 0.502174 | − | 0.864767i | \(-0.332534\pi\) | ||||
0.502174 | + | 0.864767i | \(0.332534\pi\) | |||||||
\(32\) | −861.090 | − | 861.090i | −0.840908 | − | 0.840908i | ||||
\(33\) | −1404.73 | + | 1404.73i | −1.28993 | + | 1.28993i | ||||
\(34\) | 1500.08i | 1.29765i | ||||||||
\(35\) | −143.966 | − | 440.055i | −0.117523 | − | 0.359229i | ||||
\(36\) | 4856.02 | 3.74693 | ||||||||
\(37\) | 925.201 | + | 925.201i | 0.675822 | + | 0.675822i | 0.959052 | − | 0.283230i | \(-0.0914059\pi\) |
−0.283230 | + | 0.959052i | \(0.591406\pi\) | |||||||
\(38\) | 2094.63 | − | 2094.63i | 1.45057 | − | 1.45057i | ||||
\(39\) | 733.431i | 0.482203i | ||||||||
\(40\) | 3547.76 | − | 1160.66i | 2.21735 | − | 0.725414i | ||||
\(41\) | −2299.21 | −1.36776 | −0.683881 | − | 0.729594i | \(-0.739709\pi\) | ||||
−0.683881 | + | 0.729594i | \(0.739709\pi\) | |||||||
\(42\) | 1388.35 | + | 1388.35i | 0.787049 | + | 0.787049i | ||||
\(43\) | −1190.20 | + | 1190.20i | −0.643701 | + | 0.643701i | −0.951463 | − | 0.307763i | \(-0.900420\pi\) |
0.307763 | + | 0.951463i | \(0.400420\pi\) | |||||||
\(44\) | − | 4972.17i | − | 2.56827i | ||||||
\(45\) | −1500.33 | + | 2959.32i | −0.740902 | + | 1.46139i | ||||
\(46\) | 2177.05 | 1.02885 | ||||||||
\(47\) | −1550.35 | − | 1550.35i | −0.701832 | − | 0.701832i | 0.262972 | − | 0.964804i | \(-0.415297\pi\) |
−0.964804 | + | 0.262972i | \(0.915297\pi\) | |||||||
\(48\) | −5141.28 | + | 5141.28i | −2.23146 | + | 2.23146i | ||||
\(49\) | 343.000i | 0.142857i | ||||||||
\(50\) | −690.938 | + | 4479.44i | −0.276375 | + | 1.79177i | ||||
\(51\) | 3024.03 | 1.16264 | ||||||||
\(52\) | −1298.02 | − | 1298.02i | −0.480036 | − | 0.480036i | ||||
\(53\) | 645.219 | − | 645.219i | 0.229697 | − | 0.229697i | −0.582869 | − | 0.812566i | \(-0.698070\pi\) |
0.812566 | + | 0.582869i | \(0.198070\pi\) | |||||||
\(54\) | − | 5482.73i | − | 1.88022i | ||||||
\(55\) | 3030.10 | + | 1536.21i | 1.00169 | + | 0.507839i | ||||
\(56\) | −2765.29 | −0.881789 | ||||||||
\(57\) | −4222.57 | − | 4222.57i | −1.29965 | − | 1.29965i | ||||
\(58\) | −1002.79 | + | 1002.79i | −0.298096 | + | 0.298096i | ||||
\(59\) | 2295.44i | 0.659419i | 0.944082 | + | 0.329710i | \(0.106951\pi\) | ||||
−0.944082 | + | 0.329710i | \(0.893049\pi\) | |||||||
\(60\) | −4158.03 | − | 12709.7i | −1.15501 | − | 3.53047i | ||||
\(61\) | 3198.88 | 0.859682 | 0.429841 | − | 0.902905i | \(-0.358570\pi\) | ||||
0.429841 | + | 0.902905i | \(0.358570\pi\) | |||||||
\(62\) | 4949.28 | + | 4949.28i | 1.28753 | + | 1.28753i | ||||
\(63\) | 1738.03 | − | 1738.03i | 0.437901 | − | 0.437901i | ||||
\(64\) | − | 873.373i | − | 0.213226i | ||||||
\(65\) | 1192.07 | − | 389.989i | 0.282146 | − | 0.0923052i | ||||
\(66\) | −14406.5 | −3.30728 | ||||||||
\(67\) | −6113.48 | − | 6113.48i | −1.36188 | − | 1.36188i | −0.871520 | − | 0.490360i | \(-0.836865\pi\) |
−0.490360 | − | 0.871520i | \(-0.663135\pi\) | |||||||
\(68\) | −5351.89 | + | 5351.89i | −1.15742 | + | 1.15742i | ||||
\(69\) | − | 4388.73i | − | 0.921808i | ||||||
\(70\) | 1518.30 | − | 2994.77i | 0.309857 | − | 0.611177i | ||||
\(71\) | 740.397 | 0.146875 | 0.0734375 | − | 0.997300i | \(-0.476603\pi\) | ||||
0.0734375 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(72\) | 14012.1 | + | 14012.1i | 2.70295 | + | 2.70295i | ||||
\(73\) | 1763.21 | − | 1763.21i | 0.330870 | − | 0.330870i | −0.522047 | − | 0.852917i | \(-0.674831\pi\) |
0.852917 | + | 0.522047i | \(0.174831\pi\) | |||||||
\(74\) | 9488.56i | 1.73275i | ||||||||
\(75\) | 9030.11 | + | 1392.86i | 1.60535 | + | 0.247620i | ||||
\(76\) | 14946.1 | 2.58762 | ||||||||
\(77\) | −1779.60 | − | 1779.60i | −0.300152 | − | 0.300152i | ||||
\(78\) | −3760.91 | + | 3760.91i | −0.618165 | + | 0.618165i | ||||
\(79\) | 8409.12i | 1.34740i | 0.739005 | + | 0.673700i | \(0.235296\pi\) | ||||
−0.739005 | + | 0.673700i | \(0.764704\pi\) | |||||||
\(80\) | 11090.1 | + | 5622.48i | 1.73282 | + | 0.878513i | ||||
\(81\) | −302.630 | −0.0461256 | ||||||||
\(82\) | −11790.0 | − | 11790.0i | −1.75342 | − | 1.75342i | ||||
\(83\) | 5894.49 | − | 5894.49i | 0.855637 | − | 0.855637i | −0.135183 | − | 0.990821i | \(-0.543162\pi\) |
0.990821 | + | 0.135183i | \(0.0431623\pi\) | |||||||
\(84\) | 9906.53i | 1.40399i | ||||||||
\(85\) | −1607.97 | − | 4915.04i | −0.222557 | − | 0.680282i | ||||
\(86\) | −12206.3 | −1.65040 | ||||||||
\(87\) | 2021.54 | + | 2021.54i | 0.267081 | + | 0.267081i | ||||
\(88\) | 14347.2 | − | 14347.2i | 1.85269 | − | 1.85269i | ||||
\(89\) | − | 4763.09i | − | 0.601324i | −0.953731 | − | 0.300662i | \(-0.902792\pi\) | ||
0.953731 | − | 0.300662i | \(-0.0972076\pi\) | |||||||
\(90\) | −22868.3 | + | 7481.47i | −2.82325 | + | 0.923638i | ||||
\(91\) | −929.153 | −0.112203 | ||||||||
\(92\) | 7767.12 | + | 7767.12i | 0.917666 | + | 0.917666i | ||||
\(93\) | 9977.27 | − | 9977.27i | 1.15357 | − | 1.15357i | ||||
\(94\) | − | 15899.8i | − | 1.79944i | ||||||
\(95\) | −4617.78 | + | 9108.34i | −0.511666 | + | 1.00923i | ||||
\(96\) | −17802.6 | −1.93170 | ||||||||
\(97\) | 687.835 | + | 687.835i | 0.0731039 | + | 0.0731039i | 0.742713 | − | 0.669609i | \(-0.233539\pi\) |
−0.669609 | + | 0.742713i | \(0.733539\pi\) | |||||||
\(98\) | −1758.85 | + | 1758.85i | −0.183137 | + | 0.183137i | ||||
\(99\) | 18034.9i | 1.84011i | ||||||||
\(100\) | −18446.5 | + | 13516.3i | −1.84465 | + | 1.35163i | ||||
\(101\) | −10449.3 | −1.02434 | −0.512172 | − | 0.858883i | \(-0.671159\pi\) | ||||
−0.512172 | + | 0.858883i | \(0.671159\pi\) | |||||||
\(102\) | 15506.7 | + | 15506.7i | 1.49046 | + | 1.49046i | ||||
\(103\) | 8531.35 | − | 8531.35i | 0.804161 | − | 0.804161i | −0.179582 | − | 0.983743i | \(-0.557474\pi\) |
0.983743 | + | 0.179582i | \(0.0574744\pi\) | |||||||
\(104\) | − | 7490.90i | − | 0.692576i | ||||||
\(105\) | −6037.16 | − | 3060.74i | −0.547588 | − | 0.277619i | ||||
\(106\) | 6617.16 | 0.588925 | ||||||||
\(107\) | −7239.61 | − | 7239.61i | −0.632336 | − | 0.632336i | 0.316318 | − | 0.948653i | \(-0.397553\pi\) |
−0.948653 | + | 0.316318i | \(0.897553\pi\) | |||||||
\(108\) | 19560.9 | − | 19560.9i | 1.67703 | − | 1.67703i | ||||
\(109\) | − | 12097.6i | − | 1.01823i | −0.860699 | − | 0.509115i | \(-0.829973\pi\) | ||
0.860699 | − | 0.509115i | \(-0.170027\pi\) | |||||||
\(110\) | 7660.41 | + | 23415.3i | 0.633091 | + | 1.93515i | ||||
\(111\) | 19128.0 | 1.55247 | ||||||||
\(112\) | −6513.27 | − | 6513.27i | −0.519234 | − | 0.519234i | ||||
\(113\) | −11639.0 | + | 11639.0i | −0.911507 | + | 0.911507i | −0.996391 | − | 0.0848839i | \(-0.972948\pi\) |
0.0848839 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(114\) | − | 43305.3i | − | 3.33220i | ||||||
\(115\) | −7133.12 | + | 2333.63i | −0.539367 | + | 0.176456i | ||||
\(116\) | −7155.39 | −0.531762 | ||||||||
\(117\) | 4708.15 | + | 4708.15i | 0.343937 | + | 0.343937i | ||||
\(118\) | −11770.6 | + | 11770.6i | −0.845349 | + | 0.845349i | ||||
\(119\) | 3831.01i | 0.270533i | ||||||||
\(120\) | 24675.9 | − | 48672.0i | 1.71361 | − | 3.38000i | ||||
\(121\) | 3825.30 | 0.261273 | ||||||||
\(122\) | 16403.3 | + | 16403.3i | 1.10208 | + | 1.10208i | ||||
\(123\) | −23767.4 | + | 23767.4i | −1.57098 | + | 1.57098i | ||||
\(124\) | 35315.3i | 2.29678i | ||||||||
\(125\) | −2537.75 | − | 15417.5i | −0.162416 | − | 0.986722i | ||||
\(126\) | 17824.7 | 1.12274 | ||||||||
\(127\) | 12421.7 | + | 12421.7i | 0.770148 | + | 0.770148i | 0.978132 | − | 0.207985i | \(-0.0666904\pi\) |
−0.207985 | + | 0.978132i | \(0.566690\pi\) | |||||||
\(128\) | −9298.93 | + | 9298.93i | −0.567562 | + | 0.567562i | ||||
\(129\) | 24606.8i | 1.47868i | ||||||||
\(130\) | 8112.53 | + | 4112.92i | 0.480031 | + | 0.243368i | ||||
\(131\) | −12976.3 | −0.756151 | −0.378076 | − | 0.925775i | \(-0.623414\pi\) | ||||
−0.378076 | + | 0.925775i | \(0.623414\pi\) | |||||||
\(132\) | −51398.4 | − | 51398.4i | −2.94986 | − | 2.94986i | ||||
\(133\) | 5349.39 | − | 5349.39i | 0.302414 | − | 0.302414i | ||||
\(134\) | − | 62697.9i | − | 3.49175i | ||||||
\(135\) | 5877.07 | + | 17964.2i | 0.322473 | + | 0.985691i | ||||
\(136\) | −30885.9 | −1.66987 | ||||||||
\(137\) | −13425.8 | − | 13425.8i | −0.715316 | − | 0.715316i | 0.252326 | − | 0.967642i | \(-0.418804\pi\) |
−0.967642 | + | 0.252326i | \(0.918804\pi\) | |||||||
\(138\) | 22504.7 | − | 22504.7i | 1.18172 | − | 1.18172i | ||||
\(139\) | 21541.5i | 1.11493i | 0.830201 | + | 0.557464i | \(0.188225\pi\) | ||||
−0.830201 | + | 0.557464i | \(0.811775\pi\) | |||||||
\(140\) | 16101.4 | − | 5267.63i | 0.821499 | − | 0.268757i | ||||
\(141\) | −32052.6 | −1.61222 | ||||||||
\(142\) | 3796.64 | + | 3796.64i | 0.188288 | + | 0.188288i | ||||
\(143\) | 4820.76 | − | 4820.76i | 0.235745 | − | 0.235745i | ||||
\(144\) | 66007.3i | 3.18322i | ||||||||
\(145\) | 2210.74 | − | 4360.58i | 0.105148 | − | 0.207400i | ||||
\(146\) | 18082.9 | 0.848325 | ||||||||
\(147\) | 3545.67 | + | 3545.67i | 0.164083 | + | 0.164083i | ||||
\(148\) | −33852.6 | + | 33852.6i | −1.54550 | + | 1.54550i | ||||
\(149\) | − | 23088.6i | − | 1.03998i | −0.854173 | − | 0.519989i | \(-0.825936\pi\) | ||
0.854173 | − | 0.519989i | \(-0.174064\pi\) | |||||||
\(150\) | 39162.6 | + | 53447.3i | 1.74056 | + | 2.37544i | ||||
\(151\) | 37589.4 | 1.64858 | 0.824292 | − | 0.566165i | \(-0.191574\pi\) | ||||
0.824292 | + | 0.566165i | \(0.191574\pi\) | |||||||
\(152\) | 43127.2 | + | 43127.2i | 1.86665 | + | 1.86665i | ||||
\(153\) | 19412.3 | − | 19412.3i | 0.829265 | − | 0.829265i | ||||
\(154\) | − | 18251.0i | − | 0.769564i | ||||||
\(155\) | −21521.6 | − | 10911.1i | −0.895799 | − | 0.454156i | ||||
\(156\) | −26835.8 | −1.10272 | ||||||||
\(157\) | −9237.11 | − | 9237.11i | −0.374746 | − | 0.374746i | 0.494457 | − | 0.869202i | \(-0.335367\pi\) |
−0.869202 | + | 0.494457i | \(0.835367\pi\) | |||||||
\(158\) | −43120.6 | + | 43120.6i | −1.72731 | + | 1.72731i | ||||
\(159\) | − | 13339.6i | − | 0.527651i | ||||||
\(160\) | 9466.21 | + | 28935.0i | 0.369774 | + | 1.13027i | ||||
\(161\) | 5559.89 | 0.214494 | ||||||||
\(162\) | −1551.84 | − | 1551.84i | −0.0591311 | − | 0.0591311i | ||||
\(163\) | 15066.0 | − | 15066.0i | 0.567052 | − | 0.567052i | −0.364249 | − | 0.931302i | \(-0.618674\pi\) |
0.931302 | + | 0.364249i | \(0.118674\pi\) | |||||||
\(164\) | − | 84126.7i | − | 3.12785i | ||||||
\(165\) | 47203.0 | − | 15442.6i | 1.73381 | − | 0.567223i | ||||
\(166\) | 60451.9 | 2.19378 | ||||||||
\(167\) | 10051.7 | + | 10051.7i | 0.360416 | + | 0.360416i | 0.863966 | − | 0.503550i | \(-0.167973\pi\) |
−0.503550 | + | 0.863966i | \(0.667973\pi\) | |||||||
\(168\) | −28585.4 | + | 28585.4i | −1.01281 | + | 1.01281i | ||||
\(169\) | 26044.0i | 0.911873i | ||||||||
\(170\) | 16958.1 | − | 33449.0i | 0.586785 | − | 1.15740i | ||||
\(171\) | −54212.2 | −1.85398 | ||||||||
\(172\) | −43548.8 | − | 43548.8i | −1.47204 | − | 1.47204i | ||||
\(173\) | −21678.9 | + | 21678.9i | −0.724345 | + | 0.724345i | −0.969487 | − | 0.245142i | \(-0.921165\pi\) |
0.245142 | + | 0.969487i | \(0.421165\pi\) | |||||||
\(174\) | 20732.2i | 0.684774i | ||||||||
\(175\) | −1764.56 | + | 11439.9i | −0.0576183 | + | 0.373547i | ||||
\(176\) | 67586.0 | 2.18188 | ||||||||
\(177\) | 23728.5 | + | 23728.5i | 0.757396 | + | 0.757396i | ||||
\(178\) | 24424.3 | − | 24424.3i | 0.770873 | − | 0.770873i | ||||
\(179\) | 18170.8i | 0.567111i | 0.958956 | + | 0.283556i | \(0.0915141\pi\) | ||||
−0.958956 | + | 0.283556i | \(0.908486\pi\) | |||||||
\(180\) | −108280. | − | 54896.1i | −3.34197 | − | 1.69432i | ||||
\(181\) | −43196.5 | −1.31853 | −0.659267 | − | 0.751909i | \(-0.729133\pi\) | ||||
−0.659267 | + | 0.751909i | \(0.729133\pi\) | |||||||
\(182\) | −4764.55 | − | 4764.55i | −0.143840 | − | 0.143840i | ||||
\(183\) | 33067.5 | − | 33067.5i | 0.987415 | − | 0.987415i | ||||
\(184\) | 44824.2i | 1.32397i | ||||||||
\(185\) | −10171.0 | − | 31089.3i | −0.297180 | − | 0.908381i | ||||
\(186\) | 102324. | 2.95767 | ||||||||
\(187\) | −19876.6 | − | 19876.6i | −0.568406 | − | 0.568406i | ||||
\(188\) | 56726.3 | − | 56726.3i | 1.60498 | − | 1.60498i | ||||
\(189\) | − | 14002.2i | − | 0.391987i | ||||||
\(190\) | −70385.3 | + | 23026.8i | −1.94973 | + | 0.637863i | ||||
\(191\) | 22892.9 | 0.627529 | 0.313764 | − | 0.949501i | \(-0.398410\pi\) | ||||
0.313764 | + | 0.949501i | \(0.398410\pi\) | |||||||
\(192\) | −9028.25 | − | 9028.25i | −0.244907 | − | 0.244907i | ||||
\(193\) | −37038.1 | + | 37038.1i | −0.994338 | + | 0.994338i | −0.999984 | − | 0.00564628i | \(-0.998203\pi\) |
0.00564628 | + | 0.999984i | \(0.498203\pi\) | |||||||
\(194\) | 7054.21i | 0.187433i | ||||||||
\(195\) | 8291.26 | − | 16354.1i | 0.218047 | − | 0.430087i | ||||
\(196\) | −12550.2 | −0.326691 | ||||||||
\(197\) | −2584.45 | − | 2584.45i | −0.0665940 | − | 0.0665940i | 0.673025 | − | 0.739619i | \(-0.264994\pi\) |
−0.739619 | + | 0.673025i | \(0.764994\pi\) | |||||||
\(198\) | −92480.3 | + | 92480.3i | −2.35895 | + | 2.35895i | ||||
\(199\) | − | 21774.1i | − | 0.549837i | −0.961468 | − | 0.274919i | \(-0.911349\pi\) | ||
0.961468 | − | 0.274919i | \(-0.0886509\pi\) | |||||||
\(200\) | −92229.0 | − | 14226.0i | −2.30573 | − | 0.355650i | ||||
\(201\) | −126393. | −3.12846 | ||||||||
\(202\) | −53582.5 | − | 53582.5i | −1.31317 | − | 1.31317i | ||||
\(203\) | −2561.00 | + | 2561.00i | −0.0621466 | + | 0.0621466i | ||||
\(204\) | 110647.i | 2.65877i | ||||||||
\(205\) | 51267.8 | + | 25992.0i | 1.21994 | + | 0.618488i | ||||
\(206\) | 87494.7 | 2.06180 | ||||||||
\(207\) | −28172.8 | − | 28172.8i | −0.657489 | − | 0.657489i | ||||
\(208\) | 17643.8 | − | 17643.8i | 0.407817 | − | 0.407817i | ||||
\(209\) | 55508.9i | 1.27078i | ||||||||
\(210\) | −15262.6 | − | 46652.6i | −0.346090 | − | 1.05788i | ||||
\(211\) | 75363.5 | 1.69276 | 0.846382 | − | 0.532576i | \(-0.178776\pi\) | ||||
0.846382 | + | 0.532576i | \(0.178776\pi\) | |||||||
\(212\) | 23608.2 | + | 23608.2i | 0.525280 | + | 0.525280i | ||||
\(213\) | 7653.65 | − | 7653.65i | 0.168698 | − | 0.168698i | ||||
\(214\) | − | 74247.1i | − | 1.62126i | ||||||
\(215\) | 39994.1 | − | 13084.2i | 0.865205 | − | 0.283055i | ||||
\(216\) | 112886. | 2.41955 | ||||||||
\(217\) | 12639.8 | + | 12639.8i | 0.268423 | + | 0.268423i | ||||
\(218\) | 62034.4 | − | 62034.4i | 1.30533 | − | 1.30533i | ||||
\(219\) | − | 36453.4i | − | 0.760063i | ||||||
\(220\) | −56209.1 | + | 110870.i | −1.16135 | + | 2.29069i | ||||
\(221\) | −10377.8 | −0.212482 | ||||||||
\(222\) | 98085.4 | + | 98085.4i | 1.99021 | + | 1.99021i | ||||
\(223\) | −272.650 | + | 272.650i | −0.00548271 | + | 0.00548271i | −0.709843 | − | 0.704360i | \(-0.751234\pi\) |
0.704360 | + | 0.709843i | \(0.251234\pi\) | |||||||
\(224\) | − | 22553.3i | − | 0.449484i | ||||||
\(225\) | 66908.7 | − | 49026.2i | 1.32165 | − | 0.968418i | ||||
\(226\) | −119366. | −2.33703 | ||||||||
\(227\) | −14283.0 | − | 14283.0i | −0.277184 | − | 0.277184i | 0.554800 | − | 0.831984i | \(-0.312795\pi\) |
−0.831984 | + | 0.554800i | \(0.812795\pi\) | |||||||
\(228\) | 154501. | − | 154501.i | 2.97209 | − | 2.97209i | ||||
\(229\) | 34740.0i | 0.662458i | 0.943550 | + | 0.331229i | \(0.107463\pi\) | ||||
−0.943550 | + | 0.331229i | \(0.892537\pi\) | |||||||
\(230\) | −48544.0 | − | 24611.0i | −0.917655 | − | 0.465237i | ||||
\(231\) | −36792.2 | −0.689497 | ||||||||
\(232\) | −20647.0 | − | 20647.0i | −0.383601 | − | 0.383601i | ||||
\(233\) | −12274.1 | + | 12274.1i | −0.226088 | + | 0.226088i | −0.811056 | − | 0.584968i | \(-0.801107\pi\) |
0.584968 | + | 0.811056i | \(0.301107\pi\) | |||||||
\(234\) | 48285.2i | 0.881825i | ||||||||
\(235\) | 17043.4 | + | 52096.0i | 0.308618 | + | 0.943340i | ||||
\(236\) | −83988.8 | −1.50799 | ||||||||
\(237\) | 86927.0 | + | 86927.0i | 1.54760 | + | 1.54760i | ||||
\(238\) | −19644.8 | + | 19644.8i | −0.346812 | + | 0.346812i | ||||
\(239\) | 94956.1i | 1.66237i | 0.555997 | + | 0.831184i | \(0.312336\pi\) | ||||
−0.555997 | + | 0.831184i | \(0.687664\pi\) | |||||||
\(240\) | 172761. | − | 56519.5i | 2.99933 | − | 0.981242i | ||||
\(241\) | 44563.2 | 0.767260 | 0.383630 | − | 0.923487i | \(-0.374674\pi\) | ||||
0.383630 | + | 0.923487i | \(0.374674\pi\) | |||||||
\(242\) | 19615.5 | + | 19615.5i | 0.334942 | + | 0.334942i | ||||
\(243\) | 40174.6 | − | 40174.6i | 0.680361 | − | 0.680361i | ||||
\(244\) | 117045.i | 1.96596i | ||||||||
\(245\) | 3877.53 | − | 7648.23i | 0.0645986 | − | 0.127417i | ||||
\(246\) | −243751. | −4.02788 | ||||||||
\(247\) | 14491.0 | + | 14491.0i | 0.237522 | + | 0.237522i | ||||
\(248\) | −101903. | + | 101903.i | −1.65685 | + | 1.65685i | ||||
\(249\) | − | 121865.i | − | 1.96554i | ||||||
\(250\) | 66045.5 | − | 92071.8i | 1.05673 | − | 1.47315i | ||||
\(251\) | −29296.1 | −0.465010 | −0.232505 | − | 0.972595i | \(-0.574692\pi\) | ||||
−0.232505 | + | 0.972595i | \(0.574692\pi\) | |||||||
\(252\) | 63593.5 | + | 63593.5i | 1.00141 | + | 1.00141i | ||||
\(253\) | −28846.6 | + | 28846.6i | −0.450665 | + | 0.450665i | ||||
\(254\) | 127393.i | 1.97460i | ||||||||
\(255\) | −67429.9 | − | 34185.9i | −1.03698 | − | 0.525734i | ||||
\(256\) | −109341. | −1.66841 | ||||||||
\(257\) | −26697.7 | − | 26697.7i | −0.404210 | − | 0.404210i | 0.475504 | − | 0.879714i | \(-0.342266\pi\) |
−0.879714 | + | 0.475504i | \(0.842266\pi\) | |||||||
\(258\) | −126180. | + | 126180.i | −1.89561 | + | 1.89561i | ||||
\(259\) | 24232.5i | 0.361242i | ||||||||
\(260\) | 14269.5 | + | 43617.0i | 0.211087 | + | 0.645223i | ||||
\(261\) | 25953.9 | 0.380997 | ||||||||
\(262\) | −66540.4 | − | 66540.4i | −0.969355 | − | 0.969355i | ||||
\(263\) | −69822.4 | + | 69822.4i | −1.00945 | + | 1.00945i | −0.00949086 | + | 0.999955i | \(0.503021\pi\) |
−0.999955 | + | 0.00949086i | \(0.996979\pi\) | |||||||
\(264\) | − | 296621.i | − | 4.25593i | ||||||
\(265\) | −21681.2 | + | 7093.08i | −0.308739 | + | 0.101005i | ||||
\(266\) | 54861.6 | 0.775364 | ||||||||
\(267\) | −49237.1 | − | 49237.1i | −0.690669 | − | 0.690669i | ||||
\(268\) | 223689. | − | 223689.i | 3.11440 | − | 3.11440i | ||||
\(269\) | − | 73355.9i | − | 1.01375i | −0.862020 | − | 0.506875i | \(-0.830801\pi\) | ||
0.862020 | − | 0.506875i | \(-0.169199\pi\) | |||||||
\(270\) | −61981.0 | + | 122254.i | −0.850219 | + | 1.67701i | ||||
\(271\) | 125134. | 1.70388 | 0.851939 | − | 0.523642i | \(-0.175427\pi\) | ||||
0.851939 | + | 0.523642i | \(0.175427\pi\) | |||||||
\(272\) | −72747.6 | − | 72747.6i | −0.983288 | − | 0.983288i | ||||
\(273\) | −9604.87 | + | 9604.87i | −0.128874 | + | 0.128874i | ||||
\(274\) | − | 137690.i | − | 1.83401i | ||||||
\(275\) | −50198.8 | − | 68509.0i | −0.663785 | − | 0.905904i | ||||
\(276\) | 160581. | 2.10803 | ||||||||
\(277\) | 44216.3 | + | 44216.3i | 0.576266 | + | 0.576266i | 0.933872 | − | 0.357607i | \(-0.116407\pi\) |
−0.357607 | + | 0.933872i | \(0.616407\pi\) | |||||||
\(278\) | −110461. | + | 110461.i | −1.42929 | + | 1.42929i | ||||
\(279\) | − | 128095.i | − | 1.64560i | ||||||
\(280\) | 61660.5 | + | 31260.9i | 0.786486 | + | 0.398736i | ||||
\(281\) | 148338. | 1.87862 | 0.939312 | − | 0.343065i | \(-0.111465\pi\) | ||||
0.939312 | + | 0.343065i | \(0.111465\pi\) | |||||||
\(282\) | −164360. | − | 164360.i | −2.06680 | − | 2.06680i | ||||
\(283\) | −31339.4 | + | 31339.4i | −0.391307 | + | 0.391307i | −0.875153 | − | 0.483846i | \(-0.839239\pi\) |
0.483846 | + | 0.875153i | \(0.339239\pi\) | |||||||
\(284\) | 27090.7i | 0.335880i | ||||||||
\(285\) | 46419.9 | + | 141890.i | 0.571498 | + | 1.74688i | ||||
\(286\) | 49440.1 | 0.604432 | ||||||||
\(287\) | −30110.0 | − | 30110.0i | −0.365550 | − | 0.365550i | ||||
\(288\) | −114281. | + | 114281.i | −1.37781 | + | 1.37781i | ||||
\(289\) | − | 40731.9i | − | 0.487685i | ||||||
\(290\) | 33696.7 | − | 11024.0i | 0.400674 | − | 0.131082i | ||||
\(291\) | 14220.6 | 0.167932 | ||||||||
\(292\) | 64514.8 | + | 64514.8i | 0.756648 | + | 0.756648i | ||||
\(293\) | 65192.3 | − | 65192.3i | 0.759383 | − | 0.759383i | −0.216827 | − | 0.976210i | \(-0.569571\pi\) |
0.976210 | + | 0.216827i | \(0.0695708\pi\) | |||||||
\(294\) | 36363.2i | 0.420695i | ||||||||
\(295\) | 25949.4 | − | 51183.8i | 0.298183 | − | 0.588150i | ||||
\(296\) | −195364. | −2.22978 | ||||||||
\(297\) | 72647.9 | + | 72647.9i | 0.823588 | + | 0.823588i | ||||
\(298\) | 118394. | − | 118394.i | 1.33321 | − | 1.33321i | ||||
\(299\) | 15061.2i | 0.168468i | ||||||||
\(300\) | −50964.1 | + | 330407.i | −0.566268 | + | 3.67119i | ||||
\(301\) | −31173.3 | −0.344072 | ||||||||
\(302\) | 192752. | + | 192752.i | 2.11342 | + | 2.11342i | ||||
\(303\) | −108017. | + | 108017.i | −1.17654 | + | 1.17654i | ||||
\(304\) | 203161.i | 2.19833i | ||||||||
\(305\) | −71328.7 | − | 36162.5i | −0.766769 | − | 0.388740i | ||||
\(306\) | 199086. | 2.12617 | ||||||||
\(307\) | −67430.3 | − | 67430.3i | −0.715448 | − | 0.715448i | 0.252221 | − | 0.967670i | \(-0.418839\pi\) |
−0.967670 | + | 0.252221i | \(0.918839\pi\) | |||||||
\(308\) | 65114.5 | − | 65114.5i | 0.686398 | − | 0.686398i | ||||
\(309\) | − | 176381.i | − | 1.84729i | ||||||
\(310\) | −54408.8 | − | 166310.i | −0.566169 | − | 1.73059i | ||||
\(311\) | 8860.75 | 0.0916114 | 0.0458057 | − | 0.998950i | \(-0.485414\pi\) | ||||
0.0458057 | + | 0.998950i | \(0.485414\pi\) | |||||||
\(312\) | −77435.1 | − | 77435.1i | −0.795479 | − | 0.795479i | ||||
\(313\) | −104602. | + | 104602.i | −1.06771 | + | 1.06771i | −0.0701733 | + | 0.997535i | \(0.522355\pi\) |
−0.997535 | + | 0.0701733i | \(0.977645\pi\) | |||||||
\(314\) | − | 94732.7i | − | 0.960817i | ||||||
\(315\) | −58402.6 | + | 19106.6i | −0.588588 | + | 0.192559i | ||||
\(316\) | −307685. | −3.08129 | ||||||||
\(317\) | 40820.0 | + | 40820.0i | 0.406213 | + | 0.406213i | 0.880416 | − | 0.474203i | \(-0.157264\pi\) |
−0.474203 | + | 0.880416i | \(0.657264\pi\) | |||||||
\(318\) | 68403.0 | − | 68403.0i | 0.676427 | − | 0.676427i | ||||
\(319\) | − | 26574.6i | − | 0.261148i | ||||||
\(320\) | −9873.26 | + | 19474.5i | −0.0964186 | + | 0.190181i | ||||
\(321\) | −149675. | −1.45258 | ||||||||
\(322\) | 28510.2 | + | 28510.2i | 0.274972 | + | 0.274972i | ||||
\(323\) | 59748.1 | − | 59748.1i | 0.572689 | − | 0.572689i | ||||
\(324\) | − | 11073.1i | − | 0.105482i | ||||||
\(325\) | −30989.5 | − | 4780.02i | −0.293392 | − | 0.0452546i | ||||
\(326\) | 154512. | 1.45388 | ||||||||
\(327\) | −125055. | − | 125055.i | −1.16952 | − | 1.16952i | ||||
\(328\) | 242749. | − | 242749.i | 2.25636 | − | 2.25636i | ||||
\(329\) | − | 40606.1i | − | 0.375145i | ||||||
\(330\) | 321237. | + | 162862.i | 2.94983 | + | 1.49552i | ||||
\(331\) | −14561.0 | −0.132903 | −0.0664514 | − | 0.997790i | \(-0.521168\pi\) | ||||
−0.0664514 | + | 0.997790i | \(0.521168\pi\) | |||||||
\(332\) | 215676. | + | 215676.i | 1.95671 | + | 1.95671i | ||||
\(333\) | 122789. | − | 122789.i | 1.10732 | − | 1.10732i | ||||
\(334\) | 103087.i | 0.924079i | ||||||||
\(335\) | 67207.2 | + | 205430.i | 0.598862 | + | 1.83052i | ||||
\(336\) | −134658. | −1.19276 | ||||||||
\(337\) | −52044.1 | − | 52044.1i | −0.458259 | − | 0.458259i | 0.439824 | − | 0.898084i | \(-0.355041\pi\) |
−0.898084 | + | 0.439824i | \(0.855041\pi\) | |||||||
\(338\) | −133549. | + | 133549.i | −1.16898 | + | 1.16898i | ||||
\(339\) | 240631.i | 2.09388i | ||||||||
\(340\) | 179838. | − | 58834.9i | 1.55570 | − | 0.508952i | ||||
\(341\) | −131159. | −1.12795 | ||||||||
\(342\) | −277992. | − | 277992.i | −2.37673 | − | 2.37673i | ||||
\(343\) | −4491.86 | + | 4491.86i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 251321.i | − | 2.12379i | ||||||
\(345\) | −49613.5 | + | 97860.0i | −0.416832 | + | 0.822180i | ||||
\(346\) | −222332. | −1.85716 | ||||||||
\(347\) | 17334.3 | + | 17334.3i | 0.143962 | + | 0.143962i | 0.775414 | − | 0.631453i | \(-0.217541\pi\) |
−0.631453 | + | 0.775414i | \(0.717541\pi\) | |||||||
\(348\) | −73966.8 | + | 73966.8i | −0.610771 | + | 0.610771i | ||||
\(349\) | 125838.i | 1.03314i | 0.856244 | + | 0.516572i | \(0.172792\pi\) | ||||
−0.856244 | + | 0.516572i | \(0.827208\pi\) | |||||||
\(350\) | −67710.2 | + | 49613.4i | −0.552736 | + | 0.405008i | ||||
\(351\) | 37930.5 | 0.307875 | ||||||||
\(352\) | 117014. | + | 117014.i | 0.944394 | + | 0.944394i | ||||
\(353\) | 58739.2 | − | 58739.2i | 0.471388 | − | 0.471388i | −0.430976 | − | 0.902364i | \(-0.641830\pi\) |
0.902364 | + | 0.430976i | \(0.141830\pi\) | |||||||
\(354\) | 243351.i | 1.94190i | ||||||||
\(355\) | −16509.4 | − | 8370.01i | −0.131001 | − | 0.0664155i | ||||
\(356\) | 174279. | 1.37513 | ||||||||
\(357\) | 39602.0 | + | 39602.0i | 0.310729 | + | 0.310729i | ||||
\(358\) | −93177.0 | + | 93177.0i | −0.727014 | + | 0.727014i | ||||
\(359\) | 131534.i | 1.02059i | 0.860000 | + | 0.510294i | \(0.170463\pi\) | ||||
−0.860000 | + | 0.510294i | \(0.829537\pi\) | |||||||
\(360\) | −154039. | − | 470846.i | −1.18857 | − | 3.63307i | ||||
\(361\) | −36536.2 | −0.280355 | ||||||||
\(362\) | −221505. | − | 221505.i | −1.69031 | − | 1.69031i | ||||
\(363\) | 39543.0 | − | 39543.0i | 0.300094 | − | 0.300094i | ||||
\(364\) | − | 33997.2i | − | 0.256590i | ||||||
\(365\) | −59248.7 | + | 19383.5i | −0.444727 | + | 0.145494i | ||||
\(366\) | 339130. | 2.53165 | ||||||||
\(367\) | 13662.1 | + | 13662.1i | 0.101434 | + | 0.101434i | 0.756003 | − | 0.654568i | \(-0.227150\pi\) |
−0.654568 | + | 0.756003i | \(0.727150\pi\) | |||||||
\(368\) | −105577. | + | 105577.i | −0.779607 | + | 0.779607i | ||||
\(369\) | 305143.i | 2.24104i | ||||||||
\(370\) | 107266. | − | 211576.i | 0.783534 | − | 1.54548i | ||||
\(371\) | 16899.3 | 0.122778 | ||||||||
\(372\) | 365062. | + | 365062.i | 2.63804 | + | 2.63804i | ||||
\(373\) | 155910. | − | 155910.i | 1.12061 | − | 1.12061i | 0.128964 | − | 0.991649i | \(-0.458835\pi\) |
0.991649 | − | 0.128964i | \(-0.0411652\pi\) | |||||||
\(374\) | − | 203848.i | − | 1.45735i | ||||||
\(375\) | −185608. | − | 133141.i | −1.31988 | − | 0.946783i | ||||
\(376\) | 327369. | 2.31559 | ||||||||
\(377\) | −6937.49 | − | 6937.49i | −0.0488112 | − | 0.0488112i | ||||
\(378\) | 71800.8 | − | 71800.8i | 0.502511 | − | 0.502511i | ||||
\(379\) | 74194.8i | 0.516530i | 0.966074 | + | 0.258265i | \(0.0831507\pi\) | ||||
−0.966074 | + | 0.258265i | \(0.916849\pi\) | |||||||
\(380\) | −333269. | − | 168962.i | −2.30796 | − | 1.17010i | ||||
\(381\) | 256812. | 1.76915 | ||||||||
\(382\) | 117391. | + | 117391.i | 0.804467 | + | 0.804467i | ||||
\(383\) | 153589. | − | 153589.i | 1.04704 | − | 1.04704i | 0.0482041 | − | 0.998838i | \(-0.484650\pi\) |
0.998838 | − | 0.0482041i | \(-0.0153498\pi\) | |||||||
\(384\) | 192250.i | 1.30378i | ||||||||
\(385\) | 19563.6 | + | 59799.5i | 0.131986 | + | 0.403437i | ||||
\(386\) | −379851. | −2.54940 | ||||||||
\(387\) | 157959. | + | 157959.i | 1.05469 | + | 1.05469i | ||||
\(388\) | −25167.5 | + | 25167.5i | −0.167177 | + | 0.167177i | ||||
\(389\) | 5566.71i | 0.0367874i | 0.999831 | + | 0.0183937i | \(0.00585523\pi\) | ||||
−0.999831 | + | 0.0183937i | \(0.994145\pi\) | |||||||
\(390\) | 126377. | − | 41344.8i | 0.830883 | − | 0.271827i | ||||
\(391\) | 62099.2 | 0.406193 | ||||||||
\(392\) | −36213.7 | − | 36213.7i | −0.235668 | − | 0.235668i | ||||
\(393\) | −134139. | + | 134139.i | −0.868501 | + | 0.868501i | ||||
\(394\) | − | 26505.2i | − | 0.170742i | ||||||
\(395\) | 95063.0 | − | 187507.i | 0.609281 | − | 1.20177i | ||||
\(396\) | −659888. | −4.20804 | ||||||||
\(397\) | −88916.2 | − | 88916.2i | −0.564157 | − | 0.564157i | 0.366329 | − | 0.930486i | \(-0.380615\pi\) |
−0.930486 | + | 0.366329i | \(0.880615\pi\) | |||||||
\(398\) | 111654. | − | 111654.i | 0.704869 | − | 0.704869i | ||||
\(399\) | − | 110596.i | − | 0.694693i | ||||||
\(400\) | −183726. | − | 250741.i | −1.14829 | − | 1.56713i | ||||
\(401\) | 140901. | 0.876242 | 0.438121 | − | 0.898916i | \(-0.355644\pi\) | ||||
0.438121 | + | 0.898916i | \(0.355644\pi\) | |||||||
\(402\) | −648122. | − | 648122.i | −4.01056 | − | 4.01056i | ||||
\(403\) | −34239.9 | + | 34239.9i | −0.210825 | + | 0.210825i | ||||
\(404\) | − | 382335.i | − | 2.34251i | ||||||
\(405\) | 6748.05 | + | 3421.16i | 0.0411404 | + | 0.0208575i | ||||
\(406\) | −26264.8 | −0.159339 | ||||||||
\(407\) | −125726. | − | 125726.i | −0.758992 | − | 0.758992i | ||||
\(408\) | −319274. | + | 319274.i | −1.91798 | + | 1.91798i | ||||
\(409\) | − | 36303.3i | − | 0.217020i | −0.994095 | − | 0.108510i | \(-0.965392\pi\) | ||
0.994095 | − | 0.108510i | \(-0.0346079\pi\) | |||||||
\(410\) | 129610. | + | 396176.i | 0.771032 | + | 2.35679i | ||||
\(411\) | −277570. | −1.64320 | ||||||||
\(412\) | 312157. | + | 312157.i | 1.83899 | + | 1.83899i | ||||
\(413\) | −30060.6 | + | 30060.6i | −0.176237 | + | 0.176237i | ||||
\(414\) | − | 288931.i | − | 1.68575i | ||||||
\(415\) | −198071. | + | 64799.8i | −1.15007 | + | 0.376251i | ||||
\(416\) | 61094.8 | 0.353035 | ||||||||
\(417\) | 222679. | + | 222679.i | 1.28058 | + | 1.28058i | ||||
\(418\) | −284641. | + | 284641.i | −1.62909 | + | 1.62909i | ||||
\(419\) | − | 135974.i | − | 0.774510i | −0.921973 | − | 0.387255i | \(-0.873423\pi\) | ||
0.921973 | − | 0.387255i | \(-0.126577\pi\) | |||||||
\(420\) | 111991. | − | 220896.i | 0.634869 | − | 1.25225i | ||||
\(421\) | −48464.2 | −0.273437 | −0.136718 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136718 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(422\) | 386452. | + | 386452.i | 2.17005 | + | 2.17005i | ||||
\(423\) | −205757. | + | 205757.i | −1.14993 | + | 1.14993i | ||||
\(424\) | 136243.i | 0.757851i | ||||||||
\(425\) | −19708.6 | + | 127773.i | −0.109113 | + | 0.707396i | ||||
\(426\) | 78493.4 | 0.432528 | ||||||||
\(427\) | 41891.9 | + | 41891.9i | 0.229760 | + | 0.229760i | ||||
\(428\) | 264893. | − | 264893.i | 1.44605 | − | 1.44605i | ||||
\(429\) | − | 99666.5i | − | 0.541545i | ||||||
\(430\) | 272177. | + | 137990.i | 1.47202 | + | 0.746293i | ||||
\(431\) | 103330. | 0.556251 | 0.278126 | − | 0.960545i | \(-0.410287\pi\) | ||||
0.278126 | + | 0.960545i | \(0.410287\pi\) | |||||||
\(432\) | 265889. | + | 265889.i | 1.42473 | + | 1.42473i | ||||
\(433\) | −166967. | + | 166967.i | −0.890541 | + | 0.890541i | −0.994574 | − | 0.104033i | \(-0.966825\pi\) |
0.104033 | + | 0.994574i | \(0.466825\pi\) | |||||||
\(434\) | 129629.i | 0.688215i | ||||||||
\(435\) | −22223.3 | − | 67929.2i | −0.117444 | − | 0.358987i | ||||
\(436\) | 442644. | 2.32853 | ||||||||
\(437\) | −86711.5 | − | 86711.5i | −0.454061 | − | 0.454061i | ||||
\(438\) | 186927. | − | 186927.i | 0.974370 | − | 0.974370i | ||||
\(439\) | − | 153188.i | − | 0.794870i | −0.917630 | − | 0.397435i | \(-0.869900\pi\) | ||
0.917630 | − | 0.397435i | \(-0.130100\pi\) | |||||||
\(440\) | −482108. | + | 157723.i | −2.49022 | + | 0.814687i | ||||
\(441\) | 45521.8 | 0.234068 | ||||||||
\(442\) | −53215.9 | − | 53215.9i | −0.272393 | − | 0.272393i | ||||
\(443\) | 193497. | − | 193497.i | 0.985977 | − | 0.985977i | −0.0139263 | − | 0.999903i | \(-0.504433\pi\) |
0.999903 | + | 0.0139263i | \(0.00443303\pi\) | |||||||
\(444\) | 699883.i | 3.55026i | ||||||||
\(445\) | −53845.5 | + | 106208.i | −0.271913 | + | 0.536334i | ||||
\(446\) | −2796.21 | −0.0140572 | ||||||||
\(447\) | −238672. | − | 238672.i | −1.19450 | − | 1.19450i | ||||
\(448\) | 11437.5 | − | 11437.5i | 0.0569870 | − | 0.0569870i | ||||
\(449\) | 197644.i | 0.980371i | 0.871618 | + | 0.490185i | \(0.163071\pi\) | ||||
−0.871618 | + | 0.490185i | \(0.836929\pi\) | |||||||
\(450\) | 594495. | + | 91698.8i | 2.93578 | + | 0.452834i | ||||
\(451\) | 312441. | 1.53608 | ||||||||
\(452\) | −425866. | − | 425866.i | −2.08447 | − | 2.08447i | ||||
\(453\) | 388570. | − | 388570.i | 1.89353 | − | 1.89353i | ||||
\(454\) | − | 146482.i | − | 0.710677i | ||||||
\(455\) | 20718.3 | + | 10503.8i | 0.100076 | + | 0.0507371i | ||||
\(456\) | 891631. | 4.28801 | ||||||||
\(457\) | −112416. | − | 112416.i | −0.538264 | − | 0.538264i | 0.384755 | − | 0.923019i | \(-0.374286\pi\) |
−0.923019 | + | 0.384755i | \(0.874286\pi\) | |||||||
\(458\) | −178141. | + | 178141.i | −0.849244 | + | 0.849244i | ||||
\(459\) | − | 156392.i | − | 0.742317i | ||||||
\(460\) | −85386.2 | − | 260997.i | −0.403526 | − | 1.23344i | ||||
\(461\) | 99283.0 | 0.467168 | 0.233584 | − | 0.972337i | \(-0.424955\pi\) | ||||
0.233584 | + | 0.972337i | \(0.424955\pi\) | |||||||
\(462\) | −188665. | − | 188665.i | −0.883907 | − | 0.883907i | ||||
\(463\) | −102537. | + | 102537.i | −0.478319 | + | 0.478319i | −0.904594 | − | 0.426275i | \(-0.859826\pi\) |
0.426275 | + | 0.904594i | \(0.359826\pi\) | |||||||
\(464\) | − | 97262.2i | − | 0.451761i | ||||||
\(465\) | −335264. | + | 109683.i | −1.55053 | + | 0.507263i | ||||
\(466\) | −125879. | −0.579671 | ||||||||
\(467\) | 265905. | + | 265905.i | 1.21925 | + | 1.21925i | 0.967895 | + | 0.251353i | \(0.0808755\pi\) |
0.251353 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(468\) | −172268. | + | 172268.i | −0.786528 | + | 0.786528i | ||||
\(469\) | − | 160122.i | − | 0.727956i | ||||||
\(470\) | −179744. | + | 354535.i | −0.813689 | + | 1.60496i | ||||
\(471\) | −190972. | −0.860851 | ||||||||
\(472\) | −242351. | − | 242351.i | −1.08783 | − | 1.08783i | ||||
\(473\) | 161738. | − | 161738.i | 0.722917 | − | 0.722917i | ||||
\(474\) | 891495.i | 3.96791i | ||||||||
\(475\) | 205935. | − | 150895.i | 0.912731 | − | 0.668788i | ||||
\(476\) | −140175. | −0.618665 | ||||||||
\(477\) | −85631.2 | − | 85631.2i | −0.376353 | − | 0.376353i | ||||
\(478\) | −486920. | + | 486920.i | −2.13109 | + | 2.13109i | ||||
\(479\) | − | 246167.i | − | 1.07290i | −0.843932 | − | 0.536449i | \(-0.819765\pi\) | ||
0.843932 | − | 0.536449i | \(-0.180235\pi\) | |||||||
\(480\) | 396962. | + | 201254.i | 1.72293 | + | 0.873497i | ||||
\(481\) | −65643.4 | −0.283727 | ||||||||
\(482\) | 228513. | + | 228513.i | 0.983596 | + | 0.983596i | ||||
\(483\) | 57473.9 | − | 57473.9i | 0.246363 | − | 0.246363i | ||||
\(484\) | 139966.i | 0.597490i | ||||||||
\(485\) | −7561.57 | − | 23113.2i | −0.0321461 | − | 0.0982598i | ||||
\(486\) | 412018. | 1.74439 | ||||||||
\(487\) | −47449.1 | − | 47449.1i | −0.200065 | − | 0.200065i | 0.599963 | − | 0.800028i | \(-0.295182\pi\) |
−0.800028 | + | 0.599963i | \(0.795182\pi\) | |||||||
\(488\) | −337735. | + | 337735.i | −1.41820 | + | 1.41820i | ||||
\(489\) | − | 311482.i | − | 1.30261i | ||||||
\(490\) | 59102.2 | − | 19335.5i | 0.246157 | − | 0.0805311i | ||||
\(491\) | 138021. | 0.572508 | 0.286254 | − | 0.958154i | \(-0.407590\pi\) | ||||
0.286254 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(492\) | −869637. | − | 869637.i | −3.59259 | − | 3.59259i | ||||
\(493\) | −28604.1 | + | 28604.1i | −0.117689 | + | 0.117689i | ||||
\(494\) | 148615.i | 0.608987i | ||||||||
\(495\) | 203881. | − | 402144.i | 0.832081 | − | 1.64124i | ||||
\(496\) | −480037. | −1.95124 | ||||||||
\(497\) | 9696.09 | + | 9696.09i | 0.0392540 | + | 0.0392540i | ||||
\(498\) | 624905. | − | 624905.i | 2.51974 | − | 2.51974i | ||||
\(499\) | − | 450282.i | − | 1.80835i | −0.427158 | − | 0.904177i | \(-0.640485\pi\) | ||
0.427158 | − | 0.904177i | \(-0.359515\pi\) | |||||||
\(500\) | 564119. | − | 92854.7i | 2.25648 | − | 0.371419i | ||||
\(501\) | 207812. | 0.827935 | ||||||||
\(502\) | −150226. | − | 150226.i | −0.596124 | − | 0.596124i | ||||
\(503\) | −269041. | + | 269041.i | −1.06337 | + | 1.06337i | −0.0655153 | + | 0.997852i | \(0.520869\pi\) |
−0.997852 | + | 0.0655153i | \(0.979131\pi\) | |||||||
\(504\) | 367000.i | 1.44479i | ||||||||
\(505\) | 233000. | + | 118127.i | 0.913635 | + | 0.463198i | ||||
\(506\) | −295841. | −1.15547 | ||||||||
\(507\) | 269223. | + | 269223.i | 1.04736 | + | 1.04736i | ||||
\(508\) | −454503. | + | 454503.i | −1.76120 | + | 1.76120i | ||||
\(509\) | 91831.8i | 0.354452i | 0.984170 | + | 0.177226i | \(0.0567123\pi\) | ||||
−0.984170 | + | 0.177226i | \(0.943288\pi\) | |||||||
\(510\) | −170470. | − | 521069.i | −0.655401 | − | 2.00334i | ||||
\(511\) | 46181.3 | 0.176858 | ||||||||
\(512\) | −411899. | − | 411899.i | −1.57127 | − | 1.57127i | ||||
\(513\) | −218376. | + | 218376.i | −0.829795 | + | 0.829795i | ||||
\(514\) | − | 273803.i | − | 1.03636i | ||||||
\(515\) | −286677. | + | 93787.6i | −1.08088 | + | 0.353615i | ||||
\(516\) | −900348. | −3.38151 | ||||||||
\(517\) | 210678. | + | 210678.i | 0.788202 | + | 0.788202i | ||||
\(518\) | −124260. | + | 124260.i | −0.463098 | + | 0.463098i | ||||
\(519\) | 448200.i | 1.66394i | ||||||||
\(520\) | −84682.7 | + | 167032.i | −0.313176 | + | 0.617723i | ||||
\(521\) | −317145. | −1.16838 | −0.584189 | − | 0.811618i | \(-0.698587\pi\) | ||||
−0.584189 | + | 0.811618i | \(0.698587\pi\) | |||||||
\(522\) | 133087. | + | 133087.i | 0.488422 | + | 0.488422i | ||||
\(523\) | 201425. | − | 201425.i | 0.736394 | − | 0.736394i | −0.235484 | − | 0.971878i | \(-0.575668\pi\) |
0.971878 | + | 0.235484i | \(0.0756676\pi\) | |||||||
\(524\) | − | 474796.i | − | 1.72920i | ||||||
\(525\) | 100016. | + | 136497.i | 0.362869 | + | 0.495228i | ||||
\(526\) | −716075. | −2.58814 | ||||||||
\(527\) | 141175. | + | 141175.i | 0.508321 | + | 0.508321i | ||||
\(528\) | 698652. | − | 698652.i | 2.50607 | − | 2.50607i | ||||
\(529\) | 189717.i | 0.677947i | ||||||||
\(530\) | −147550. | − | 74805.3i | −0.525275 | − | 0.266306i | ||||
\(531\) | 304642. | 1.08044 | ||||||||
\(532\) | 195731. | + | 195731.i | 0.691571 | + | 0.691571i | ||||
\(533\) | 81564.9 | − | 81564.9i | 0.287110 | − | 0.287110i | ||||
\(534\) | − | 504960.i | − | 1.77082i | ||||||
\(535\) | 79587.1 | + | 243271.i | 0.278058 | + | 0.849930i | ||||
\(536\) | 1.29091e6 | 4.49332 | ||||||||
\(537\) | 187836. | + | 187836.i | 0.651373 | + | 0.651373i | ||||
\(538\) | 376157. | − | 376157.i | 1.29959 | − | 1.29959i | ||||
\(539\) | − | 46610.5i | − | 0.160438i | ||||||
\(540\) | −657301. | + | 215039.i | −2.25412 | + | 0.737443i | ||||
\(541\) | −288032. | −0.984115 | −0.492058 | − | 0.870563i | \(-0.663755\pi\) | ||||
−0.492058 | + | 0.870563i | \(0.663755\pi\) | |||||||
\(542\) | 641669. | + | 641669.i | 2.18430 | + | 2.18430i | ||||
\(543\) | −446532. | + | 446532.i | −1.51444 | + | 1.51444i | ||||
\(544\) | − | 251901.i | − | 0.851202i | ||||||
\(545\) | −136760. | + | 269752.i | −0.460433 | + | 0.908181i | ||||
\(546\) | −98504.4 | −0.330423 | ||||||||
\(547\) | 84502.3 | + | 84502.3i | 0.282419 | + | 0.282419i | 0.834073 | − | 0.551654i | \(-0.186003\pi\) |
−0.551654 | + | 0.834073i | \(0.686003\pi\) | |||||||
\(548\) | 491241. | − | 491241.i | 1.63581 | − | 1.63581i | ||||
\(549\) | − | 424544.i | − | 1.40857i | ||||||
\(550\) | 93892.0 | − | 608714.i | 0.310387 | − | 2.01228i | ||||
\(551\) | 79882.2 | 0.263116 | ||||||||
\(552\) | 463358. | + | 463358.i | 1.52068 | + | 1.52068i | ||||
\(553\) | −110124. | + | 110124.i | −0.360108 | + | 0.360108i | ||||
\(554\) | 453468.i | 1.47750i | ||||||||
\(555\) | −426517. | − | 216237.i | −1.38468 | − | 0.702013i | ||||
\(556\) | −788192. | −2.54966 | ||||||||
\(557\) | −83519.3 | − | 83519.3i | −0.269201 | − | 0.269201i | 0.559577 | − | 0.828778i | \(-0.310964\pi\) |
−0.828778 | + | 0.559577i | \(0.810964\pi\) | |||||||
\(558\) | 656851. | − | 656851.i | 2.10959 | − | 2.10959i | ||||
\(559\) | − | 84445.4i | − | 0.270242i | ||||||
\(560\) | 71602.2 | + | 218864.i | 0.228323 | + | 0.697908i | ||||
\(561\) | −410937. | −1.30572 | ||||||||
\(562\) | 760653. | + | 760653.i | 2.40832 | + | 2.40832i | ||||
\(563\) | −377217. | + | 377217.i | −1.19008 | + | 1.19008i | −0.213030 | + | 0.977046i | \(0.568333\pi\) |
−0.977046 | + | 0.213030i | \(0.931667\pi\) | |||||||
\(564\) | − | 1.17279e6i | − | 3.68689i | ||||||
\(565\) | 391104. | − | 127951.i | 1.22517 | − | 0.400818i | ||||
\(566\) | −321406. | −1.00328 | ||||||||
\(567\) | −3963.18 | − | 3963.18i | −0.0123276 | − | 0.0123276i | ||||
\(568\) | −78170.6 | + | 78170.6i | −0.242296 | + | 0.242296i | ||||
\(569\) | 4157.76i | 0.0128421i | 0.999979 | + | 0.00642103i | \(0.00204389\pi\) | ||||
−0.999979 | + | 0.00642103i | \(0.997956\pi\) | |||||||
\(570\) | −489555. | + | 965623.i | −1.50679 | + | 2.97206i | ||||
\(571\) | 281259. | 0.862650 | 0.431325 | − | 0.902197i | \(-0.358046\pi\) | ||||
0.431325 | + | 0.902197i | \(0.358046\pi\) | |||||||
\(572\) | 176389. | + | 176389.i | 0.539112 | + | 0.539112i | ||||
\(573\) | 236649. | − | 236649.i | 0.720768 | − | 0.720768i | ||||
\(574\) | − | 308798.i | − | 0.937240i | ||||||
\(575\) | 185436. | + | 28602.8i | 0.560864 | + | 0.0865114i | ||||
\(576\) | −115911. | −0.349365 | ||||||||
\(577\) | −363376. | − | 363376.i | −1.09145 | − | 1.09145i | −0.995374 | − | 0.0960790i | \(-0.969370\pi\) |
−0.0960790 | − | 0.995374i | \(-0.530630\pi\) | |||||||
\(578\) | 208867. | − | 208867.i | 0.625192 | − | 0.625192i | ||||
\(579\) | 765742.i | 2.28415i | ||||||||
\(580\) | 159551. | + | 80889.9i | 0.474290 | + | 0.240457i | ||||
\(581\) | 154386. | 0.457357 | ||||||||
\(582\) | 72921.0 | + | 72921.0i | 0.215281 | + | 0.215281i | ||||
\(583\) | −87679.3 | + | 87679.3i | −0.257965 | + | 0.257965i | ||||
\(584\) | 372317.i | 1.09166i | ||||||||
\(585\) | −51758.0 | − | 158207.i | −0.151240 | − | 0.462289i | ||||
\(586\) | 668591. | 1.94700 | ||||||||
\(587\) | −90438.2 | − | 90438.2i | −0.262467 | − | 0.262467i | 0.563588 | − | 0.826056i | \(-0.309420\pi\) |
−0.826056 | + | 0.563588i | \(0.809420\pi\) | |||||||
\(588\) | −129734. | + | 129734.i | −0.375231 | + | 0.375231i | ||||
\(589\) | − | 394258.i | − | 1.13645i | ||||||
\(590\) | 395526. | − | 129398.i | 1.13624 | − | 0.371726i | ||||
\(591\) | −53432.0 | −0.152977 | ||||||||
\(592\) | −460154. | − | 460154.i | −1.31298 | − | 1.31298i | ||||
\(593\) | 54345.8 | − | 54345.8i | 0.154546 | − | 0.154546i | −0.625599 | − | 0.780145i | \(-0.715145\pi\) |
0.780145 | + | 0.625599i | \(0.215145\pi\) | |||||||
\(594\) | 745053.i | 2.11161i | ||||||||
\(595\) | 43308.7 | − | 85424.1i | 0.122332 | − | 0.241294i | ||||
\(596\) | 844798. | 2.37826 | ||||||||
\(597\) | −225084. | − | 225084.i | −0.631532 | − | 0.631532i | ||||
\(598\) | −77231.4 | + | 77231.4i | −0.215969 | + | 0.215969i | ||||
\(599\) | − | 49282.3i | − | 0.137353i | −0.997639 | − | 0.0686764i | \(-0.978122\pi\) | ||
0.997639 | − | 0.0686764i | \(-0.0218776\pi\) | |||||||
\(600\) | −1.10045e6 | + | 806335.i | −3.05681 | + | 2.23982i | ||||
\(601\) | −520219. | −1.44025 | −0.720123 | − | 0.693846i | \(-0.755915\pi\) | ||||
−0.720123 | + | 0.693846i | \(0.755915\pi\) | |||||||
\(602\) | −159852. | − | 159852.i | −0.441087 | − | 0.441087i | ||||
\(603\) | −811360. | + | 811360.i | −2.23141 | + | 2.23141i | ||||
\(604\) | 1.37537e6i | 3.77005i | ||||||||
\(605\) | −85296.8 | − | 43244.1i | −0.233035 | − | 0.118145i | ||||
\(606\) | −1.10779e6 | −3.01656 | ||||||||
\(607\) | 151266. | + | 151266.i | 0.410547 | + | 0.410547i | 0.881929 | − | 0.471382i | \(-0.156245\pi\) |
−0.471382 | + | 0.881929i | \(0.656245\pi\) | |||||||
\(608\) | −351740. | + | 351740.i | −0.951511 | + | 0.951511i | ||||
\(609\) | 52947.3i | 0.142761i | ||||||||
\(610\) | −180326. | − | 551198.i | −0.484618 | − | 1.48132i | ||||
\(611\) | 109998. | 0.294647 | ||||||||
\(612\) | 710284. | + | 710284.i | 1.89640 | + | 1.89640i | ||||
\(613\) | 55744.1 | − | 55744.1i | 0.148347 | − | 0.148347i | −0.629032 | − | 0.777379i | \(-0.716549\pi\) |
0.777379 | + | 0.629032i | \(0.216549\pi\) | |||||||
\(614\) | − | 691543.i | − | 1.83435i | ||||||
\(615\) | 798652. | − | 261282.i | 2.11158 | − | 0.690812i | ||||
\(616\) | 375777. | 0.990306 | ||||||||
\(617\) | −298648. | − | 298648.i | −0.784493 | − | 0.784493i | 0.196093 | − | 0.980585i | \(-0.437175\pi\) |
−0.980585 | + | 0.196093i | \(0.937175\pi\) | |||||||
\(618\) | 904453. | − | 904453.i | 2.36815 | − | 2.36815i | ||||
\(619\) | 345096.i | 0.900656i | 0.892863 | + | 0.450328i | \(0.148693\pi\) | ||||
−0.892863 | + | 0.450328i | \(0.851307\pi\) | |||||||
\(620\) | 399231. | − | 787462.i | 1.03858 | − | 2.04855i | ||||
\(621\) | −226969. | −0.588551 | ||||||||
\(622\) | 45436.5 | + | 45436.5i | 0.117442 | + | 0.117442i | ||||
\(623\) | 62376.5 | − | 62376.5i | 0.160711 | − | 0.160711i | ||||
\(624\) | − | 364776.i | − | 0.936822i | ||||||
\(625\) | −117705. | + | 372469.i | −0.301324 | + | 0.953522i | ||||
\(626\) | −1.07277e6 | −2.73752 | ||||||||
\(627\) | 573808. | + | 573808.i | 1.45959 | + | 1.45959i | ||||
\(628\) | 337980. | − | 337980.i | 0.856983 | − | 0.856983i | ||||
\(629\) | 270656.i | 0.684095i | ||||||||
\(630\) | −397455. | − | 201503.i | −1.00140 | − | 0.507693i | ||||
\(631\) | −184294. | −0.462864 | −0.231432 | − | 0.972851i | \(-0.574341\pi\) | ||||
−0.231432 | + | 0.972851i | \(0.574341\pi\) | |||||||
\(632\) | −887829. | − | 887829.i | −2.22277 | − | 2.22277i | ||||
\(633\) | 779050. | − | 779050.i | 1.94428 | − | 1.94428i | ||||
\(634\) | 418636.i | 1.04150i | ||||||||
\(635\) | −136555. | − | 417404.i | −0.338658 | − | 1.03516i | ||||
\(636\) | 488087. | 1.20665 | ||||||||
\(637\) | −12168.0 | − | 12168.0i | −0.0299875 | − | 0.0299875i | ||||
\(638\) | 136270. | − | 136270.i | 0.334781 | − | 0.334781i | ||||
\(639\) | − | 98262.9i | − | 0.240651i | ||||||
\(640\) | 312470. | − | 102226.i | 0.762866 | − | 0.249575i | ||||
\(641\) | −538716. | −1.31112 | −0.655562 | − | 0.755142i | \(-0.727568\pi\) | ||||
−0.655562 | + | 0.755142i | \(0.727568\pi\) | |||||||
\(642\) | −767509. | − | 767509.i | −1.86214 | − | 1.86214i | ||||
\(643\) | −95071.3 | + | 95071.3i | −0.229947 | + | 0.229947i | −0.812670 | − | 0.582724i | \(-0.801987\pi\) |
0.582724 | + | 0.812670i | \(0.301987\pi\) | |||||||
\(644\) | 203433.i | 0.490513i | ||||||||
\(645\) | 278174. | − | 548683.i | 0.668646 | − | 1.31887i | ||||
\(646\) | 612757. | 1.46833 | ||||||||
\(647\) | 90118.2 | + | 90118.2i | 0.215280 | + | 0.215280i | 0.806506 | − | 0.591226i | \(-0.201356\pi\) |
−0.591226 | + | 0.806506i | \(0.701356\pi\) | |||||||
\(648\) | 31951.4 | − | 31951.4i | 0.0760922 | − | 0.0760922i | ||||
\(649\) | − | 311929.i | − | 0.740570i | ||||||
\(650\) | −134398. | − | 183420.i | −0.318102 | − | 0.434131i | ||||
\(651\) | 261321. | 0.616611 | ||||||||
\(652\) | 551257. | + | 551257.i | 1.29676 | + | 1.29676i | ||||
\(653\) | −242315. | + | 242315.i | −0.568268 | + | 0.568268i | −0.931643 | − | 0.363375i | \(-0.881624\pi\) |
0.363375 | + | 0.931643i | \(0.381624\pi\) | |||||||
\(654\) | − | 1.28253e6i | − | 2.99855i | ||||||
\(655\) | 289346. | + | 146694.i | 0.674428 | + | 0.341924i | ||||
\(656\) | 1.14352e6 | 2.65728 | ||||||||
\(657\) | −234007. | − | 234007.i | −0.542123 | − | 0.542123i | ||||
\(658\) | 208221. | − | 208221.i | 0.480921 | − | 0.480921i | ||||
\(659\) | 682462.i | 1.57148i | 0.618559 | + | 0.785738i | \(0.287717\pi\) | ||||
−0.618559 | + | 0.785738i | \(0.712283\pi\) | |||||||
\(660\) | 565037. | + | 1.72713e6i | 1.29715 | + | 3.96494i | ||||
\(661\) | 125400. | 0.287008 | 0.143504 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143504 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(662\) | −74666.2 | − | 74666.2i | −0.170376 | − | 0.170376i | ||||
\(663\) | −107278. | + | 107278.i | −0.244053 | + | 0.244053i | ||||
\(664\) | 1.24467e6i | 2.82305i | ||||||||
\(665\) | −179755. | + | 58807.4i | −0.406478 | + | 0.132981i | ||||
\(666\) | 1.25929e6 | 2.83907 | ||||||||
\(667\) | 41512.8 | + | 41512.8i | 0.0933104 | + | 0.0933104i | ||||
\(668\) | −367784. | + | 367784.i | −0.824215 | + | 0.824215i | ||||
\(669\) | 5636.88i | 0.0125947i | ||||||||
\(670\) | −708784. | + | 1.39804e6i | −1.57893 | + | 3.11437i | ||||
\(671\) | −434698. | −0.965479 | ||||||||
\(672\) | −233139. | − | 233139.i | −0.516269 | − | 0.516269i | ||||
\(673\) | 103115. | − | 103115.i | 0.227662 | − | 0.227662i | −0.584053 | − | 0.811715i | \(-0.698534\pi\) |
0.811715 | + | 0.584053i | \(0.198534\pi\) | |||||||
\(674\) | − | 533747.i | − | 1.17494i | ||||||
\(675\) | 72034.0 | − | 467006.i | 0.158099 | − | 1.02498i | ||||
\(676\) | −952936. | −2.08531 | ||||||||
\(677\) | −620376. | − | 620376.i | −1.35356 | − | 1.35356i | −0.881643 | − | 0.471917i | \(-0.843562\pi\) |
−0.471917 | − | 0.881643i | \(-0.656438\pi\) | |||||||
\(678\) | −1.23391e6 | + | 1.23391e6i | −2.68427 | + | 2.68427i | ||||
\(679\) | 18015.5i | 0.0390757i | ||||||||
\(680\) | 688695. | + | 349157.i | 1.48939 | + | 0.755098i | ||||
\(681\) | −295294. | −0.636736 | ||||||||
\(682\) | −672561. | − | 672561.i | −1.44598 | − | 1.44598i | ||||
\(683\) | 484076. | − | 484076.i | 1.03770 | − | 1.03770i | 0.0384396 | − | 0.999261i | \(-0.487761\pi\) |
0.999261 | − | 0.0384396i | \(-0.0122387\pi\) | |||||||
\(684\) | − | 1.98359e6i | − | 4.23976i | ||||||
\(685\) | 147593. | + | 451143.i | 0.314547 | + | 0.961465i | ||||
\(686\) | −46067.1 | −0.0978909 | ||||||||
\(687\) | 359115. | + | 359115.i | 0.760886 | + | 0.760886i | ||||
\(688\) | 591954. | − | 591954.i | 1.25058 | − | 1.25058i | ||||
\(689\) | 45778.6i | 0.0964326i | ||||||||
\(690\) | −756220. | + | 247400.i | −1.58836 | + | 0.519639i | ||||
\(691\) | −813004. | −1.70269 | −0.851347 | − | 0.524603i | \(-0.824214\pi\) | ||||
−0.851347 | + | 0.524603i | \(0.824214\pi\) | |||||||
\(692\) | −793219. | − | 793219.i | −1.65646 | − | 1.65646i | ||||
\(693\) | −236182. | + | 236182.i | −0.491791 | + | 0.491791i | ||||
\(694\) | 177775.i | 0.369106i | ||||||||
\(695\) | 243521. | − | 480334.i | 0.504159 | − | 0.994428i | ||||
\(696\) | −426864. | −0.881194 | ||||||||
\(697\) | −336302. | − | 336302.i | −0.692252 | − | 0.692252i | ||||
\(698\) | −645277. | + | 645277.i | −1.32445 | + | 1.32445i | ||||
\(699\) | 253760.i | 0.519360i | ||||||||
\(700\) | −418578. | − | 64564.3i | −0.854242 | − | 0.131764i | ||||
\(701\) | 409417. | 0.833163 | 0.416581 | − | 0.909098i | \(-0.363228\pi\) | ||||
0.416581 | + | 0.909098i | \(0.363228\pi\) | |||||||
\(702\) | 194501. | + | 194501.i | 0.394683 | + | 0.394683i | ||||
\(703\) | 377927. | − | 377927.i | 0.764712 | − | 0.764712i | ||||
\(704\) | 118683.i | 0.239466i | ||||||||
\(705\) | 714709. | + | 362346.i | 1.43797 | + | 0.729030i | ||||
\(706\) | 602410. | 1.20860 | ||||||||
\(707\) | −136842. | − | 136842.i | −0.273768 | − | 0.273768i | ||||
\(708\) | −868211. | + | 868211.i | −1.73204 | + | 1.73204i | ||||
\(709\) | − | 147502.i | − | 0.293430i | −0.989179 | − | 0.146715i | \(-0.953130\pi\) | ||
0.989179 | − | 0.146715i | \(-0.0468701\pi\) | |||||||
\(710\) | −41737.5 | − | 127578.i | −0.0827961 | − | 0.253080i | ||||
\(711\) | 1.11603e6 | 2.20768 | ||||||||
\(712\) | 502883. | + | 502883.i | 0.991990 | + | 0.991990i | ||||
\(713\) | 204886. | − | 204886.i | 0.403026 | − | 0.403026i | ||||
\(714\) | 406146.i | 0.796683i | ||||||||
\(715\) | −161991. | + | 52996.0i | −0.316868 | + | 0.103665i | ||||
\(716\) | −664860. | −1.29689 | ||||||||
\(717\) | 981583. | + | 981583.i | 1.90936 | + | 1.90936i | ||||
\(718\) | −674487. | + | 674487.i | −1.30835 | + | 1.30835i | ||||
\(719\) | 60901.4i | 0.117807i | 0.998264 | + | 0.0589033i | \(0.0187604\pi\) | ||||
−0.998264 | + | 0.0589033i | \(0.981240\pi\) | |||||||
\(720\) | 746196. | − | 1.47183e6i | 1.43942 | − | 2.83918i | ||||
\(721\) | 223450. | 0.429842 | ||||||||
\(722\) | −187352. | − | 187352.i | −0.359404 | − | 0.359404i | ||||
\(723\) | 460660. | − | 460660.i | 0.881260 | − | 0.881260i | ||||
\(724\) | − | 1.58054e6i | − | 3.01528i | ||||||
\(725\) | −98590.5 | + | 72240.4i | −0.187568 | + | 0.137437i | ||||
\(726\) | 405541. | 0.769416 | ||||||||
\(727\) | −401016. | − | 401016.i | −0.758739 | − | 0.758739i | 0.217354 | − | 0.976093i | \(-0.430257\pi\) |
−0.976093 | + | 0.217354i | \(0.930257\pi\) | |||||||
\(728\) | 98099.3 | − | 98099.3i | 0.185099 | − | 0.185099i | ||||
\(729\) | − | 855102.i | − | 1.60903i | ||||||
\(730\) | −403213. | − | 204423.i | −0.756639 | − | 0.383604i | ||||
\(731\) | −348179. | −0.651580 | ||||||||
\(732\) | 1.20992e6 | + | 1.20992e6i | 2.25806 | + | 2.25806i | ||||
\(733\) | −171074. | + | 171074.i | −0.318403 | + | 0.318403i | −0.848153 | − | 0.529751i | \(-0.822285\pi\) |
0.529751 | + | 0.848153i | \(0.322285\pi\) | |||||||
\(734\) | 140114.i | 0.260070i | ||||||||
\(735\) | −38978.6 | − | 119144.i | −0.0721524 | − | 0.220546i | ||||
\(736\) | −365581. | −0.674881 | ||||||||
\(737\) | 830766. | + | 830766.i | 1.52948 | + | 1.52948i | ||||
\(738\) | −1.56472e6 | + | 1.56472e6i | −2.87293 | + | 2.87293i | ||||
\(739\) | − | 698841.i | − | 1.27965i | −0.768522 | − | 0.639823i | \(-0.779008\pi\) | ||
0.768522 | − | 0.639823i | \(-0.220992\pi\) | |||||||
\(740\) | 1.13754e6 | − | 372151.i | 2.07732 | − | 0.679604i | ||||
\(741\) | 299593. | 0.545626 | ||||||||
\(742\) | 86657.0 | + | 86657.0i | 0.157397 | + | 0.157397i | ||||
\(743\) | −163993. | + | 163993.i | −0.297062 | + | 0.297062i | −0.839862 | − | 0.542800i | \(-0.817364\pi\) |
0.542800 | + | 0.839862i | \(0.317364\pi\) | |||||||
\(744\) | 2.10678e6i | 3.80605i | ||||||||
\(745\) | −261011. | + | 514830.i | −0.470268 | + | 0.927580i | ||||
\(746\) | 1.59896e6 | 2.87316 | ||||||||
\(747\) | −782295. | − | 782295.i | −1.40194 | − | 1.40194i | ||||
\(748\) | 727273. | − | 727273.i | 1.29985 | − | 1.29985i | ||||
\(749\) | − | 189617.i | − | 0.337998i | ||||||
\(750\) | −269040. | − | 1.63449e6i | −0.478293 | − | 2.90577i | ||||
\(751\) | 648908. | 1.15054 | 0.575272 | − | 0.817962i | \(-0.304896\pi\) | ||||
0.575272 | + | 0.817962i | \(0.304896\pi\) | |||||||
\(752\) | 771073. | + | 771073.i | 1.36352 | + | 1.36352i | ||||
\(753\) | −302840. | + | 302840.i | −0.534101 | + | 0.534101i | ||||
\(754\) | − | 71148.7i | − | 0.125148i | ||||||
\(755\) | −838169. | − | 424938.i | −1.47041 | − | 0.745473i | ||||
\(756\) | 512331. | 0.896411 | ||||||||
\(757\) | −427480. | − | 427480.i | −0.745975 | − | 0.745975i | 0.227746 | − | 0.973721i | \(-0.426865\pi\) |
−0.973721 | + | 0.227746i | \(0.926865\pi\) | |||||||
\(758\) | −380459. | + | 380459.i | −0.662170 | + | 0.662170i | ||||
\(759\) | 596387.i | 1.03525i | ||||||||
\(760\) | −474109. | − | 1.44919e6i | −0.820827 | − | 2.50899i | ||||
\(761\) | 277901. | 0.479867 | 0.239934 | − | 0.970789i | \(-0.422874\pi\) | ||||
0.239934 | + | 0.970789i | \(0.422874\pi\) | |||||||
\(762\) | 1.31689e6 | + | 1.31689e6i | 2.26798 | + | 2.26798i | ||||
\(763\) | 158428. | − | 158428.i | 0.272133 | − | 0.272133i | ||||
\(764\) | 837638.i | 1.43506i | ||||||||
\(765\) | −652307. | + | 213405.i | −1.11463 | + | 0.364654i | ||||
\(766\) | 1.57516e6 | 2.68453 | ||||||||
\(767\) | −81431.2 | − | 81431.2i | −0.138420 | − | 0.138420i | ||||
\(768\) | −1.13028e6 | + | 1.13028e6i | −1.91630 | + | 1.91630i | ||||
\(769\) | − | 347634.i | − | 0.587855i | −0.955828 | − | 0.293927i | \(-0.905038\pi\) | ||
0.955828 | − | 0.293927i | \(-0.0949624\pi\) | |||||||
\(770\) | −206323. | + | 406961.i | −0.347989 | + | 0.686391i | ||||
\(771\) | −551960. | −0.928536 | ||||||||
\(772\) | −1.35520e6 | − | 1.35520e6i | −2.27389 | − | 2.27389i | ||||
\(773\) | 264187. | − | 264187.i | 0.442132 | − | 0.442132i | −0.450596 | − | 0.892728i | \(-0.648788\pi\) |
0.892728 | + | 0.450596i | \(0.148788\pi\) | |||||||
\(774\) | 1.61998e6i | 2.70413i | ||||||||
\(775\) | 356542. | + | 486592.i | 0.593618 | + | 0.810143i | ||||
\(776\) | −145242. | −0.241196 | ||||||||
\(777\) | 250497. | + | 250497.i | 0.414916 | + | 0.414916i | ||||
\(778\) | −28545.2 | + | 28545.2i | −0.0471600 | + | 0.0471600i | ||||
\(779\) | 939184.i | 1.54766i | ||||||||
\(780\) | 598386. | + | 303372.i | 0.983541 | + | 0.498640i | ||||
\(781\) | −100613. | −0.164950 | ||||||||
\(782\) | 318435. | + | 318435.i | 0.520723 | + | 0.520723i | ||||
\(783\) | 104547. | − | 104547.i | 0.170525 | − | 0.170525i | ||||
\(784\) | − | 170593.i | − | 0.277542i | ||||||
\(785\) | 101546. | + | 310393.i | 0.164787 | + | 0.503700i | ||||
\(786\) | −1.37569e6 | −2.22677 | ||||||||
\(787\) | 228223. | + | 228223.i | 0.368477 | + | 0.368477i | 0.866921 | − | 0.498445i | \(-0.166095\pi\) |
−0.498445 | + | 0.866921i | \(0.666095\pi\) | |||||||
\(788\) | 94563.4 | − | 94563.4i | 0.152290 | − | 0.152290i | ||||
\(789\) | 1.44354e6i | 2.31886i | ||||||||
\(790\) | 1.44897e6 | − | 474037.i | 2.32170 | − | 0.759553i | ||||
\(791\) | −304845. | −0.487221 | ||||||||
\(792\) | −1.90412e6 | − | 1.90412e6i | −3.03559 | − | 3.03559i | ||||
\(793\) | −113481. | + | 113481.i | −0.180458 | + | 0.180458i | ||||
\(794\) | − | 911896.i | − | 1.44645i | ||||||
\(795\) | −150800. | + | 297446.i | −0.238599 | + | 0.470624i | ||||
\(796\) | 796702. | 1.25739 | ||||||||
\(797\) | 703348. | + | 703348.i | 1.10727 | + | 1.10727i | 0.993508 | + | 0.113763i | \(0.0362903\pi\) |
0.113763 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(798\) | 567117. | − | 567117.i | 0.890568 | − | 0.890568i | ||||
\(799\) | − | 453535.i | − | 0.710423i | ||||||
\(800\) | 116025. | − | 752208.i | 0.181290 | − | 1.17532i | ||||
\(801\) | −632140. | −0.985255 | ||||||||
\(802\) | 722515. | + | 722515.i | 1.12331 | + | 1.12331i | ||||
\(803\) | −239604. | + | 239604.i | −0.371589 | + | 0.371589i | ||||
\(804\) | − | 4.62464e6i | − | 7.15428i | ||||||
\(805\) | −123975. | − | 62853.2i | −0.191312 | − | 0.0969920i | ||||
\(806\) | −351154. | −0.540539 | ||||||||
\(807\) | −758297. | − | 758297.i | −1.16437 | − | 1.16437i | ||||
\(808\) | 1.10323e6 | − | 1.10323e6i | 1.68984 | − | 1.68984i | ||||
\(809\) | − | 117237.i | − | 0.179129i | −0.995981 | − | 0.0895646i | \(-0.971452\pi\) | ||
0.995981 | − | 0.0895646i | \(-0.0285476\pi\) | |||||||
\(810\) | 17059.8 | + | 52146.1i | 0.0260018 | + | 0.0794788i | ||||
\(811\) | −364516. | −0.554210 | −0.277105 | − | 0.960840i | \(-0.589375\pi\) | ||||
−0.277105 | + | 0.960840i | \(0.589375\pi\) | |||||||
\(812\) | −93705.5 | − | 93705.5i | −0.142119 | − | 0.142119i | ||||
\(813\) | 1.29354e6 | − | 1.29354e6i | 1.95704 | − | 1.95704i | ||||
\(814\) | − | 1.28941e6i | − | 1.94599i | ||||||
\(815\) | −506260. | + | 165625.i | −0.762182 | + | 0.249351i | ||||
\(816\) | −1.50402e6 | −2.25877 | ||||||||
\(817\) | 486176. | + | 486176.i | 0.728365 | + | 0.728365i | ||||
\(818\) | 186157. | − | 186157.i | 0.278211 | − | 0.278211i | ||||
\(819\) | 123314.i | 0.183842i | ||||||||
\(820\) | −951032. | + | 1.87586e6i | −1.41438 | + | 2.78980i | ||||
\(821\) | −437621. | −0.649249 | −0.324625 | − | 0.945843i | \(-0.605238\pi\) | ||||
−0.324625 | + | 0.945843i | \(0.605238\pi\) | |||||||
\(822\) | −1.42334e6 | − | 1.42334e6i | −2.10651 | − | 2.10651i | ||||
\(823\) | −456640. | + | 456640.i | −0.674178 | + | 0.674178i | −0.958676 | − | 0.284498i | \(-0.908173\pi\) |
0.284498 | + | 0.958676i | \(0.408173\pi\) | |||||||
\(824\) | 1.80147e6i | 2.65321i | ||||||||
\(825\) | −1.22711e6 | − | 189277.i | −1.80292 | − | 0.278093i | ||||
\(826\) | −308292. | −0.451858 | ||||||||
\(827\) | −459888. | − | 459888.i | −0.672421 | − | 0.672421i | 0.285853 | − | 0.958274i | \(-0.407723\pi\) |
−0.958274 | + | 0.285853i | \(0.907723\pi\) | |||||||
\(828\) | 1.03082e6 | − | 1.03082e6i | 1.50357 | − | 1.50357i | ||||
\(829\) | 746352.i | 1.08601i | 0.839729 | + | 0.543006i | \(0.182714\pi\) | ||||
−0.839729 | + | 0.543006i | \(0.817286\pi\) | |||||||
\(830\) | −1.34796e6 | − | 683394.i | −1.95668 | − | 0.992008i | ||||
\(831\) | 914148. | 1.32378 | ||||||||
\(832\) | 30983.1 | + | 30983.1i | 0.0447588 | + | 0.0447588i | ||||
\(833\) | −50170.2 | + | 50170.2i | −0.0723029 | + | 0.0723029i | ||||
\(834\) | 2.28373e6i | 3.28331i | ||||||||
\(835\) | −110501. | − | 337764.i | −0.158486 | − | 0.484440i | ||||
\(836\) | −2.03104e6 | −2.90607 | ||||||||
\(837\) | −515989. | − | 515989.i | −0.736529 | − | 0.736529i | ||||
\(838\) | 697251. | − | 697251.i | 0.992891 | − | 0.992891i | ||||
\(839\) | 1.11049e6i | 1.57758i | 0.614662 | + | 0.788791i | \(0.289292\pi\) | ||||
−0.614662 | + | 0.788791i | \(0.710708\pi\) | |||||||
\(840\) | 960550. | − | 314248.i | 1.36132 | − | 0.445363i | ||||
\(841\) | 669038. | 0.945929 | ||||||||
\(842\) | −248517. | − | 248517.i | −0.350535 | − | 0.350535i | ||||
\(843\) | 1.53340e6 | − | 1.53340e6i | 2.15775 | − | 2.15775i | ||||
\(844\) | 2.75751e6i | 3.87108i | ||||||||
\(845\) | 294421. | − | 580730.i | 0.412340 | − | 0.813320i | ||||
\(846\) | −2.11017e6 | −2.94834 | ||||||||
\(847\) | 50095.4 | + | 50095.4i | 0.0698283 | + | 0.0698283i | ||||
\(848\) | −320903. | + | 320903.i | −0.446254 | + | 0.446254i | ||||
\(849\) | 647924.i | 0.898894i | ||||||||
\(850\) | −756264. | + | 554139.i | −1.04673 | + | 0.766974i | ||||
\(851\) | 392799. | 0.542389 | ||||||||
\(852\) | 280043. | + | 280043.i | 0.385785 | + | 0.385785i | ||||
\(853\) | −444139. | + | 444139.i | −0.610408 | + | 0.610408i | −0.943052 | − | 0.332644i | \(-0.892059\pi\) |
0.332644 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(854\) | 429629.i | 0.589085i | ||||||||
\(855\) | 1.20883e6 | + | 612856.i | 1.65361 | + | 0.838352i | ||||
\(856\) | 1.52871e6 | 2.08630 | ||||||||
\(857\) | 609160. | + | 609160.i | 0.829411 | + | 0.829411i | 0.987435 | − | 0.158024i | \(-0.0505125\pi\) |
−0.158024 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(858\) | 511074. | − | 511074.i | 0.694239 | − | 0.694239i | ||||
\(859\) | − | 291558.i | − | 0.395129i | −0.980290 | − | 0.197564i | \(-0.936697\pi\) | ||
0.980290 | − | 0.197564i | \(-0.0633032\pi\) | |||||||
\(860\) | 478745. | + | 1.46336e6i | 0.647302 | + | 1.97859i | ||||
\(861\) | −622507. | −0.839727 | ||||||||
\(862\) | 529858. | + | 529858.i | 0.713091 | + | 0.713091i | ||||
\(863\) | −161287. | + | 161287.i | −0.216559 | + | 0.216559i | −0.807047 | − | 0.590488i | \(-0.798935\pi\) |
0.590488 | + | 0.807047i | \(0.298935\pi\) | |||||||
\(864\) | 920686.i | 1.23334i | ||||||||
\(865\) | 728472. | − | 238322.i | 0.973600 | − | 0.318517i | ||||
\(866\) | −1.71236e6 | −2.28327 | ||||||||
\(867\) | −421055. | − | 421055.i | −0.560145 | − | 0.560145i | ||||
\(868\) | −462482. | + | 462482.i | −0.613841 | + | 0.613841i | ||||
\(869\) | − | 1.14272e6i | − | 1.51322i | ||||||
\(870\) | 234373. | − | 462288.i | 0.309648 | − | 0.610764i | ||||
\(871\) | 433754. | 0.571752 | ||||||||
\(872\) | 1.27725e6 | + | 1.27725e6i | 1.67975 | + | 1.67975i | ||||
\(873\) | 91287.0 | − | 91287.0i | 0.119779 | − | 0.119779i | ||||
\(874\) | − | 889285.i | − | 1.16417i | ||||||
\(875\) | 168671. | − | 235139.i | 0.220305 | − | 0.307120i | ||||
\(876\) | 1.33381e6 | 1.73814 | ||||||||
\(877\) | −500503. | − | 500503.i | −0.650740 | − | 0.650740i | 0.302431 | − | 0.953171i | \(-0.402202\pi\) |
−0.953171 | + | 0.302431i | \(0.902202\pi\) | |||||||
\(878\) | 785524. | − | 785524.i | 1.01899 | − | 1.01899i | ||||
\(879\) | − | 1.34781e6i | − | 1.74443i | ||||||
\(880\) | −1.50704e6 | − | 764043.i | −1.94607 | − | 0.986626i | ||||
\(881\) | 1.05961e6 | 1.36519 | 0.682595 | − | 0.730797i | \(-0.260851\pi\) | ||||
0.682595 | + | 0.730797i | \(0.260851\pi\) | |||||||
\(882\) | 233428. | + | 233428.i | 0.300065 | + | 0.300065i | ||||
\(883\) | 864065. | − | 864065.i | 1.10822 | − | 1.10822i | 0.114833 | − | 0.993385i | \(-0.463367\pi\) |
0.993385 | − | 0.114833i | \(-0.0366332\pi\) | |||||||
\(884\) | − | 379719.i | − | 0.485912i | ||||||
\(885\) | −260854. | − | 797343.i | −0.333051 | − | 1.01802i | ||||
\(886\) | 1.98444e6 | 2.52796 | ||||||||
\(887\) | −224843. | − | 224843.i | −0.285780 | − | 0.285780i | 0.549629 | − | 0.835409i | \(-0.314769\pi\) |
−0.835409 | + | 0.549629i | \(0.814769\pi\) | |||||||
\(888\) | −2.01952e6 | + | 2.01952e6i | −2.56108 | + | 2.56108i | ||||
\(889\) | 325344.i | 0.411661i | ||||||||
\(890\) | −820726. | + | 268504.i | −1.03614 | + | 0.338977i | ||||
\(891\) | 41124.6 | 0.0518020 | ||||||||
\(892\) | −9976.10 | − | 9976.10i | −0.0125381 | − | 0.0125381i | ||||
\(893\) | −633288. | + | 633288.i | −0.794142 | + | 0.794142i | ||||
\(894\) | − | 2.44774e6i | − | 3.06260i | ||||||
\(895\) | 205417. | − | 405174.i | 0.256442 | − | 0.505819i | ||||
\(896\) | −243554. | −0.303374 | ||||||||
\(897\) | 155691. | + | 155691.i | 0.193499 | + | 0.193499i | ||||
\(898\) | −1.01348e6 | + | 1.01348e6i | −1.25680 | + | 1.25680i | ||||
\(899\) | 188749.i | 0.233542i | ||||||||
\(900\) | 1.79384e6 | + | 2.44815e6i | 2.21462 | + | 3.02241i | ||||
\(901\) | 188751. | 0.232509 | ||||||||
\(902\) | 1.60215e6 | + | 1.60215e6i | 1.96920 | + | 1.96920i | ||||
\(903\) | −322246. | + | 322246.i | −0.395195 | + | 0.395195i | ||||
\(904\) | − | 2.45768e6i | − | 3.00738i | ||||||
\(905\) | 963197. | + | 488326.i | 1.17603 | + | 0.596228i | ||||
\(906\) | 3.98504e6 | 4.85486 | ||||||||
\(907\) | −763805. | − | 763805.i | −0.928470 | − | 0.928470i | 0.0691372 | − | 0.997607i | \(-0.477975\pi\) |
−0.997607 | + | 0.0691372i | \(0.977975\pi\) | |||||||
\(908\) | 522607. | − | 522607.i | 0.633875 | − | 0.633875i | ||||
\(909\) | 1.38680e6i | 1.67836i | ||||||||
\(910\) | 52378.0 | + | 160102.i | 0.0632508 | + | 0.193337i | ||||
\(911\) | −36782.5 | −0.0443205 | −0.0221602 | − | 0.999754i | \(-0.507054\pi\) | ||||
−0.0221602 | + | 0.999754i | \(0.507054\pi\) | |||||||
\(912\) | 2.10012e6 | + | 2.10012e6i | 2.52496 | + | 2.52496i | ||||
\(913\) | −801006. | + | 801006.i | −0.960936 | + | 0.960936i | ||||
\(914\) | − | 1.15290e6i | − | 1.38007i | ||||||
\(915\) | −1.11116e6 | + | 363521.i | −1.32720 | + | 0.434197i | ||||
\(916\) | −1.27112e6 | −1.51493 | ||||||||
\(917\) | −169935. | − | 169935.i | −0.202090 | − | 0.202090i | ||||
\(918\) | 801953. | − | 801953.i | 0.951620 | − | 0.951620i | ||||
\(919\) | − | 1.21169e6i | − | 1.43470i | −0.696713 | − | 0.717350i | \(-0.745355\pi\) | ||
0.696713 | − | 0.717350i | \(-0.254645\pi\) | |||||||
\(920\) | 506727. | − | 999493.i | 0.598685 | − | 1.18088i | ||||
\(921\) | −1.39408e6 | −1.64350 | ||||||||
\(922\) | 509107. | + | 509107.i | 0.598890 | + | 0.598890i | ||||
\(923\) | −26265.8 | + | 26265.8i | −0.0308309 | + | 0.0308309i | ||||
\(924\) | − | 1.34621e6i | − | 1.57677i | ||||||
\(925\) | −124664. | + | 808212.i | −0.145699 | + | 0.944586i | ||||
\(926\) | −1.05158e6 | −1.22637 | ||||||||
\(927\) | −1.13225e6 | − | 1.13225e6i | −1.31760 | − | 1.31760i | ||||
\(928\) | 168394. | − | 168394.i | 0.195538 | − | 0.195538i | ||||
\(929\) | 526211.i | 0.609718i | 0.952398 | + | 0.304859i | \(0.0986093\pi\) | ||||
−0.952398 | + | 0.304859i | \(0.901391\pi\) | |||||||
\(930\) | −2.28162e6 | − | 1.15674e6i | −2.63801 | − | 1.33743i | ||||
\(931\) | 140109. | 0.161647 | ||||||||
\(932\) | −449102. | − | 449102.i | −0.517026 | − | 0.517026i | ||||
\(933\) | 91595.5 | − | 91595.5i | 0.105223 | − | 0.105223i | ||||
\(934\) | 2.72703e6i | 3.12605i | ||||||||
\(935\) | 218509. | + | 667908.i | 0.249946 | + | 0.764001i | ||||
\(936\) | −994166. | −1.13477 | ||||||||
\(937\) | −762510. | − | 762510.i | −0.868493 | − | 0.868493i | 0.123813 | − | 0.992306i | \(-0.460488\pi\) |
−0.992306 | + | 0.123813i | \(0.960488\pi\) | |||||||
\(938\) | 821079. | − | 821079.i | 0.933209 | − | 0.933209i | ||||
\(939\) | 2.16260e6i | 2.45270i | ||||||||
\(940\) | −1.90616e6 | + | 623608.i | −2.15727 | + | 0.705759i | ||||
\(941\) | −98666.8 | −0.111427 | −0.0557137 | − | 0.998447i | \(-0.517743\pi\) | ||||
−0.0557137 | + | 0.998447i | \(0.517743\pi\) | |||||||
\(942\) | −979274. | − | 979274.i | −1.10358 | − | 1.10358i | ||||
\(943\) | −488071. | + | 488071.i | −0.548857 | + | 0.548857i | ||||
\(944\) | − | 1.14165e6i | − | 1.28112i | ||||||
\(945\) | −158291. | + | 312221.i | −0.177253 | + | 0.349621i | ||||
\(946\) | 1.65873e6 | 1.85350 | ||||||||
\(947\) | 835870. | + | 835870.i | 0.932049 | + | 0.932049i | 0.997834 | − | 0.0657847i | \(-0.0209551\pi\) |
−0.0657847 | + | 0.997834i | \(0.520955\pi\) | |||||||
\(948\) | −3.18061e6 | + | 3.18061e6i | −3.53911 | + | 3.53911i | ||||
\(949\) | 125100.i | 0.138908i | ||||||||
\(950\) | 1.82977e6 | + | 282235.i | 2.02744 | + | 0.312726i | ||||
\(951\) | 843930. | 0.933137 | ||||||||
\(952\) | −404475. | − | 404475.i | −0.446291 | − | 0.446291i | ||||
\(953\) | 992061. | − | 992061.i | 1.09233 | − | 1.09233i | 0.0970474 | − | 0.995280i | \(-0.469060\pi\) |
0.995280 | − | 0.0970474i | \(-0.0309398\pi\) | |||||||
\(954\) | − | 878206.i | − | 0.964938i | ||||||
\(955\) | −510466. | − | 258798.i | −0.559707 | − | 0.283762i | ||||
\(956\) | −3.47439e6 | −3.80157 | ||||||||
\(957\) | −274708. | − | 274708.i | −0.299949 | − | 0.299949i | ||||
\(958\) | 1.26230e6 | − | 1.26230e6i | 1.37541 | − | 1.37541i | ||||
\(959\) | − | 351642.i | − | 0.382353i | ||||||
\(960\) | 99250.2 | + | 303375.i | 0.107693 | + | 0.329182i | ||||
\(961\) | 8048.05 | 0.00871453 | ||||||||
\(962\) | −336609. | − | 336609.i | −0.363727 | − | 0.363727i | ||||
\(963\) | −960816. | + | 960816.i | −1.03607 | + | 1.03607i | ||||
\(964\) | 1.63054e6i | 1.75460i | ||||||||
\(965\) | 1.24458e6 | − | 407170.i | 1.33650 | − | 0.437242i | ||||
\(966\) | 589433. | 0.631656 | ||||||||
\(967\) | 102132. | + | 102132.i | 0.109221 | + | 0.109221i | 0.759605 | − | 0.650384i | \(-0.225392\pi\) |
−0.650384 | + | 0.759605i | \(0.725392\pi\) | |||||||
\(968\) | −403873. | + | 403873.i | −0.431017 | + | 0.431017i | ||||
\(969\) | − | 1.23526e6i | − | 1.31556i | ||||||
\(970\) | 79746.1 | − | 157295.i | 0.0847551 | − | 0.167175i | ||||
\(971\) | −476996. | −0.505913 | −0.252957 | − | 0.967478i | \(-0.581403\pi\) | ||||
−0.252957 | + | 0.967478i | \(0.581403\pi\) | |||||||
\(972\) | 1.46997e6 | + | 1.46997e6i | 1.55588 | + | 1.55588i | ||||
\(973\) | −282103. | + | 282103.i | −0.297977 | + | 0.297977i | ||||
\(974\) | − | 486623.i | − | 0.512949i | ||||||
\(975\) | −369758. | + | 270933.i | −0.388963 | + | 0.285005i | ||||
\(976\) | −1.59098e6 | −1.67019 | ||||||||
\(977\) | −434620. | − | 434620.i | −0.455324 | − | 0.455324i | 0.441793 | − | 0.897117i | \(-0.354343\pi\) |
−0.897117 | + | 0.441793i | \(0.854343\pi\) | |||||||
\(978\) | 1.59723e6 | − | 1.59723e6i | 1.66989 | − | 1.66989i | ||||
\(979\) | 647260.i | 0.675326i | ||||||||
\(980\) | 279844. | + | 141877.i | 0.291383 | + | 0.147727i | ||||
\(981\) | −1.60555e6 | −1.66834 | ||||||||
\(982\) | 707748. | + | 707748.i | 0.733932 | + | 0.733932i | ||||
\(983\) | −149156. | + | 149156.i | −0.154359 | + | 0.154359i | −0.780062 | − | 0.625702i | \(-0.784812\pi\) |
0.625702 | + | 0.780062i | \(0.284812\pi\) | |||||||
\(984\) | − | 5.01869e6i | − | 5.18323i | ||||||
\(985\) | 28411.6 | + | 86844.6i | 0.0292835 | + | 0.0895097i | ||||
\(986\) | −293355. | −0.301744 | ||||||||
\(987\) | −419754. | − | 419754.i | −0.430884 | − | 0.430884i | ||||
\(988\) | −530217. | + | 530217.i | −0.543175 | + | 0.543175i | ||||
\(989\) | 505307.i | 0.516610i | ||||||||
\(990\) | 3.10760e6 | − | 1.01666e6i | 3.17069 | − | 1.03730i | ||||
\(991\) | 116777. | 0.118908 | 0.0594541 | − | 0.998231i | \(-0.481064\pi\) | ||||
0.0594541 | + | 0.998231i | \(0.481064\pi\) | |||||||
\(992\) | −831106. | − | 831106.i | −0.844565 | − | 0.844565i | ||||
\(993\) | −150520. | + | 150520.i | −0.152650 | + | 0.152650i | ||||
\(994\) | 99440.0i | 0.100644i | ||||||||
\(995\) | −246151. | + | 485520.i | −0.248631 | + | 0.490412i | ||||
\(996\) | 4.45898e6 | 4.49487 | ||||||||
\(997\) | 363823. | + | 363823.i | 0.366016 | + | 0.366016i | 0.866022 | − | 0.500006i | \(-0.166669\pi\) |
−0.500006 | + | 0.866022i | \(0.666669\pi\) | |||||||
\(998\) | 2.30897e6 | − | 2.30897e6i | 2.31824 | − | 2.31824i | ||||
\(999\) | − | 989234.i | − | 0.991215i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 35.5.g.a.22.12 | yes | 24 | |
5.2 | odd | 4 | 175.5.g.c.43.1 | 24 | |||
5.3 | odd | 4 | inner | 35.5.g.a.8.12 | ✓ | 24 | |
5.4 | even | 2 | 175.5.g.c.57.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.12 | ✓ | 24 | 5.3 | odd | 4 | inner | |
35.5.g.a.22.12 | yes | 24 | 1.1 | even | 1 | trivial | |
175.5.g.c.43.1 | 24 | 5.2 | odd | 4 | |||
175.5.g.c.57.1 | 24 | 5.4 | even | 2 |